Conference Session

First-Year Programs Division Technical Session 5B: Work-In-Progress: 5 Minute Postcard Session II

Collection

2016 ASEE Annual Conference & Exposition

Authors

Hyun J. Kwon, Andrews University

Tagged Divisions

First-Year Programs

Educ. 2007;11:89-99.[8] Morries l, Ma M, Wu PC. Agile Innovation: The Revolutionary Approach to Accelerate Success, InspireEngagement, and Ignite Creativity: Wiley; 2014.Appendix A. Rubric on grading traditional term report and web page. Performance Unacceptable Marginal Good Very Good Indicator 1 2 3 4 Organization There is no Some information Most information is Information is of Information clear plan for is logically organized in a organized in a clear, the organization sequenced. clear, logical way

Conference Session

Computers in Education Division Poster Session

Collection

2016 ASEE Annual Conference & Exposition

Authors

Todd D. Morton, Western Washington University; Ying Lin, Western Washington University

Tagged Topics

Diversity

Tagged Divisions

Computers in Education

effectiveness of the selected MCU-based platform compared to the traditionaldedicated DSP hardware, we propose to use the following assessment measures:  First, students’ feedback in the form of survey questionnaires will be collected. We plan to conduct two sets of surveys: One from students who completed the DSP class in spring 2015. In this course, the dedicated DSP hardware was used. As a comparison, we will also obtain surveys from students who will complete the DSP class in spring 2016. In this course, the MCU-based DSP hardware will be used. Such feedback will help us to assess how the students feel about the effectiveness of the proposed MCU-based platform compared to the DSP-based

Conference Session

Concurrent Paper Tracks Session II Skills Development

Collection

2016 ASEE International Forum

Authors

Saud A Ghani, Qatar University

Tagged Topics

Diversity, International Forum

ofmaturity. 3College of Engineering (CENG) – Qatar UniversityQatar University (QU) is the first national College of Education of the State of Qatar founded in1973. Hence in 1977, Qatar University was founded with four new colleges, namely Education,Humanities & Social Sciences, Sharia, Law & Islamic Studies, and Science. The College ofEngineering was later established in 1980. In its first year the college admitted 57 male and 93female students. Currently, CENG is a house of six academic departments for undergraduateprograms: Architecture and Urban Planning, Computer Engineering and Industrial Engineering,Civil Engineering, Mechanical Engineering

Conference Session

Concurrent Paper Tracks Session I Accredidation

Collection

2016 ASEE International Forum

Authors

Mandy Liu, Institute of Engineering Education Taiwan (IEET); Liang-Jenq Leu, Dept. of Civil Engineering, National Taiwan University; Charlie Than, Myanmar Engineering Council

Tagged Topics

International Forum

to take workshop trainings in carpentry, blacksmith, welding, and inmachine shop.Third Phase (1961 – 1988) After 1962, the Faculty of Engineering became an independent Institute, calledBurma Institute of Technology (BIT), with its own Rector, under the Directorate of HigherEducation, Ministry of Education. BIT was changed into RIT after about a year. Thereason for the change was that the Ministry of Education planned to open more institutesof technology in other parts of the country at a later date. RIT had its own Administrative Page 3Council and Senate, chaired by the Rector to give policy directions related to respectiveadministrative and academic matters. However, higher Administrative

Conference Session

Concurrent Paper Tracks Session II Outreach

Collection

2016 ASEE International Forum

Authors

Leslie Seawright, Texas A&M University at Qatar; Ibrahim Hassan P.E., University of Texas, Austin; Ali Darwish Alashar, Texas A&M University at Qatar

Tagged Topics

Diversity, International Forum

and planned the student meetings,worked with publishers to obtain quotes for various types of children’s books, and collected dataon the project.The division of labor and scope of the project was decided by the students themselves. Theydivided into two groups: an illustration group and a dialogue/text group. Despite these divisions,the students actually met as a whole on most occasions and discussed the book project as a team.As the students reached the mid-point in the semester, it became clear that the book would not beaccomplished using only student art. An illustrator was hired in order to take the students’concept drawings and turn them into the actual book pages.FindingsThis project was funded through a Transformative Educational

Conference Session

Classroom Practice II: Technology - and Game-Based Learning

Collection

2016 ASEE Annual Conference & Exposition

Authors

Abigail Christine Perkins, Texas A&M University; Gary T. Fry Ph.D., P.E., Texas A&M University; Carol L. Stuessy, Texas A&M University

Tagged Divisions

Educational Research and Methods

) plans by setting goals for playing and timing; (2)strategizes by deciding which strategy to use for a task or when to change a strategy; (3)regulates time use, effort, pace, or performance; and (4) regulates motivation, emotion orenvironment (i.e., volition control). The resulting sub-categories for the earthquake engineeringcontent knowledge category were: (1) interconnectivity, (2) importance of water, (3) redundancy,(4) resilience, (5) human element, (6) safety, and (7) real-life applications.When a player showed evidence on the video record for an item on the GBL checklist, we usedMicrosoft Word to code the corresponding segment of the video transcription according tochecklist categories. A Design phase focus group member and the game

Conference Session

The Intersection of Higher Ed and Industry

Collection

2016 ASEE Annual Conference & Exposition

Authors

Nikitha Sambamurthy, Purdue University - West Lafayette; Monica Farmer Cox, Purdue University - West Lafayette

Tagged Divisions

Continuing Professional Development

anenvelope that contains cut up pieces of 4 playing cards such that no single envelope contains theparts to make one whole card. The objective of the game is for teams to barter with each other inorder to become the first team to piece together the 4 cards. First, each team is given 3 minutes tosort its pieces, determine which pieces it needs to make complete cards, and develop abargaining plan. Teams are then allowed to start bartering for pieces. People can barter on theirown or as a team. When the time is up, whichever team has the most number of completed cardswins.Step 1: Identify observable attributes to evaluate. To determine the specific criterion to evaluatein each game, interviews may be conducted with hiring experts who have experience

Conference Session

International Division Technical Session 3

Collection

2016 ASEE Annual Conference & Exposition

Authors

Gholam Ali Shaykhian, Florida Institute of Technology; Jinan Ziade; Mohd A. Khairi, Najran University

Tagged Topics

Diversity

Tagged Divisions

International

practices tocarry out or avoid when attempting to form business relationships in MENA. A United Statesfederal government agency, the Overseas Private Investment Corporation (OPIC), has beeninstrumental in promoting and assisting United States multinational corporations operatingoverseas. A survey conducted in 2014 shows that 52% of multinational corporations (MNCs)surveyed aspire to increase business operations globally and only 15% planned to developleaders with cultural competence [30]. This discrepancy may lead to a loss in pool of globalleadership and a critical gap in cross-cultural skills [30]. For an organization to enhanceorganizational performance and remain globally competitive using cross-cultural understandingas an effective tool

Conference Session

K-12 & Pre-College Engineering Division: Evaluation: Impact of Curriculum for PreK-12 Engineering Education

Collection

2016 ASEE Annual Conference & Exposition

Authors

Jennifer B. Listman, New York University; Vikram Kapila, New York University

Tagged Topics

Diversity

Tagged Divisions

Pre-College Engineering Education Division

college and girls areless likely to believe that they are expected to prioritize STEM classes. Roots of these gender-specific under-expectations on the part of students’ families and potential solutions have been 28explored in STEM education research, elsewhere. While results were not corrected for multipletesting, they are useful for identifying further research questions. We plan to gather additionaldata in subsequent years, including teacher questionnaire responses, to further investigate theeffects of our challenge-based engineering programs and specific factors within our programs onstudent STEM attitudes. AcknowledgementsThis work is funded in part by the New York City Department of

Conference Session

Electrical and Computer Division Poster Session

Collection

2016 ASEE Annual Conference & Exposition

Authors

Peter M. Osterberg, University of Portland; Aziz Sukru Inan, University of Portland

Tagged Divisions

Electrical and Computer

question). These excellent evaluations along withvery positive student comments reveal that the students’ understanding, interest, and enthusiasmfor nanoelectronics and electronic conduction phenomena was greatly enhanced, making this“Bottom-Up” approach very effective in improving EE undergraduate students’ fundamentalknowledge of electronic conduction phenomena. Based on these initial assessment results, it isconcluded that incorporating Purdue University’s new “Bottom-Up” approach in our EEundergraduate curriculum is successful, and we plan to continue using it. The authors willcontinue to assess the effectiveness of this new approach in our senior-level EE analogelectronics elective course each future fall semester, going forward.Conclusion

Conference Session

Ethics Instruction in Context: Civil and Construction Engineering and Engineering Technology

Collection

2016 ASEE Annual Conference & Exposition

Authors

Hossein Ataei P.E., Syracuse University; Ossama M. Salem, University of Cincinnati

Tagged Divisions

Engineering Ethics

PROJECTCIE 475 – Civil & Environmental Engineering Senior Design Project, or capstone project, is afour-credit senior-level capstone core course. Senior students of both civil engineering andenvironmental engineering majors must take this course in order to graduate. This is a Project-Based-Learning (PBL) course where students work on planning, designing, cost estimating,scheduling and preparing a comprehensive report and final presentation for a real-world industryproject. This course is normally taken after the CIE 401. It encompasses almost all of the ABETlearning outcomes (a-k or 1-6) and, hence, engineering professionalism and ethics is covered inthe course in order to better prepare the graduating civil and environmental engineering class

Conference Session

Addressing Diversity Issues in Engineering Education

Collection

2016 ASEE Annual Conference & Exposition

Authors

Lea K Marlor, University of California, Berkeley; Catherine T. Amelink, Virginia Tech

Tagged Topics

Diversity

Tagged Divisions

Two Year College Division

process than participants. While non-participants rated themselves higherin this area, data on admission rates would suggest otherwise. Transfer Questions 6.00 5.00 4.00 3.00 2.00 1.00 0.00 To what degree do you feel prepared to apply for I understand the Admissions process (e.g., how to enrollment in a four-year institution? apply, when to apply) for the four-year institution(s) I plan to apply to. Pre Post Nonparticipants Table 2: Transfer Admissions ReportingAs a result

Collection

2016 ETLI

Authors

Wilson Gautreaux

, environmental, and societal contexts. 6. An ability to recognize the ongoing need for additional knowledge and locate, evaluate, integrate, and apply this knowledge appropriately. 7. An ability to function effectively on teams that establish goals, plan tasks, meet deadlines, and analyze risk and uncertainty. 16Responses to Proposed EAC Revisions• National Academy of Engineering and ASEE Forums• Concerns about proposed Criterion 3 • Removal of broad education, and multidisciplinary teams • Elimination of health, safety, and sustainability • Number of words about the same as in current Criterion 3 • Lumping items for

Conference Session

They need more than technical skills!

Collection

2017 ASEE Annual Conference & Exposition

Authors

Robert Prewitt Penno P.E., University of Dayton; Roger J. Crum, University of Dayton; Eddy M. Rojas, University of Dayton

Tagged Topics

Diversity

Tagged Divisions

International

, the students are introduced to engineeringresponses to earthquakes in view of the recent earthquakes that Assisi and this region of Italy areincreasingly experiencing in the modern era.Daily StructureAfter the initial week, the groups begin work on their assigned projects, employing theengineering problem-solving process described above. The weekly structure includes meetingeach day at 9:00 A.M. in a classroom setting for approximately 3 hours. During this time,groups develop a plan for the remainder of the working day and meet with faculty for guidance.Individual reviews of students’ leadership books are also typically given during this time withgeneral discussion about the various leadership models represented by the different authors

Conference Session

Engineering Economy Division Technical Session 3

Collection

2017 ASEE Annual Conference & Exposition

Authors

Tagged Topics

Diversity

Tagged Divisions

Engineering Economy

requires a car to get to the site and about 3 hours of total time including the tour and travel back and forth from campus.• Macaroon Cookie Business Expansion: This is a theoretical case based on ideas from a student capstone project where a small business company is looking at producing a new product line and they need to analyze if their expansion plans will be cost effective. No tour is provided.• HCP Laser Project – Heating and Cooling Products (HCP) is a small US based ductwork components manufacturer about 1-hour drive north of campus. A previous intern helped develop this case study which was based on the need for the company to improve cost effectiveness in terms of labor and scrap for their blank cutting process for

Conference Session

Electrical and Computer Division Technical Session 6

Collection

2017 ASEE Annual Conference & Exposition

Authors

H. Bryan Riley, Ohio University

Tagged Topics

Diversity

Tagged Divisions

Electrical and Computer

taking the required EE the capstone course. Plans are 𝑑 = 43,300𝑥1.236 (2)where: d – actual distance in cm. to continue this project and investigate related x – sensor reading performance and tradeoff matters associated with 6more sophisticated sensors, vehicle control, and [9] W. Qui, et al., “Autonomous vehicle longitudinal followingtarget recognition and identification. Longer term control based on model predictive control”, IEEE Conference

Conference Session

Analysis of Effectiveness and Impacts of Graduate Programs: Graduate Studies Division Technical Session 8

Collection

2017 ASEE Annual Conference & Exposition

Authors

Fazil T. Najafi, University of Florida; Sarah Rajkumari Jayasekaran, University of Florida

Tagged Divisions

Graduate Studies

Beta Pi. His research on passive radon-resistant new residential building construction was adapted in HB1647 building code of Florida Legislature. Najafi is a member of numerous professional societies and has served on many committees and programs, and continuously attends and presents refereed papers at international, national, and local professional meetings and conferences. Lastly, Najafi attends courses, seminars and workshops, and has developed courses, videos and software packages during his career. His areas of specialization include transportation planning and management, legal aspects, construction contract administration, and public works.Miss Sarah Rajkumari Jayasekaran

Conference Session

Efficient Authenticity: Modeling, Labs, Real-World Applications in Aerospace

Collection

2017 ASEE Annual Conference & Exposition

Authors

Richard Melnyk, U.S. Military Academy

Tagged Divisions

Aerospace

The laboratory exercise is executed over a period of two days with up to three backupdates planned for weather problems. The pilots and aircraft belong to a detachment that providesadministrative and VIP support to the Academy. Prior to the actual conduct of the lab exercisethe instructor for the course meets with the lab pilots to review administrative and logisticalrequirements and review the lab procedures. The Instructor is also a qualified helicopter pilotbut does not operate the aircraft during the course of the lab exercise in order to provide betteroversight of the students as they gather data and participate in the lab experience. The aircraft used for the labs is a UH-72A Lakota, which is a military version of theAirbus EC

Conference Session

MET Papers 2

Collection

2017 ASEE Annual Conference & Exposition

Authors

Joseph A. Untener P.E., University of Dayton

Tagged Divisions

Engineering Technology

limited technician help, and student support. For these reasons, cost andinfrastructure can be an issue for some institutions.This approach does not provide a great deal of time developing any one skill. These are BSETprograms and graduates are not technicians. For this reason, students only develop basicfamiliarity with such skills as tube flaring and pipe fitting, for example. They do not graduatewith a proficiency in hands-on technician skills. For some two-year programs, this requiredoutcome would necessitate a different approach.This multifaceted lab also takes more time for administration and planning. It is substantiallyeasier for an instructor to step through a series of activities from a standard trainer workbook or acomputer simulation

Conference Session

Community Engagement Division Technical Session 2

Collection

2017 ASEE Annual Conference & Exposition

Authors

Yashu Kang, Chung Yuan Christian University; Yao-Jen Chang, Chung Yuan Christian University; Shaou-Gang Miaou, Chung-Yuan Christian University; Chen Li-Yu, Chung Yuan Christian University; Yao-Sheng Chang, Department of Tourism and Leisure Management, Chung Chou University of Science and Technology

Tagged Topics

Diversity

Tagged Divisions

Community Engagement Division

code games for education and entertainment. However, this was thefirst effort to combine Kinect, Scratch, and Kinect2Scratch to develop interactive gamesfor children with ASD to engage in shower training.Four male and two female elementary school children with ASD (Allen, Bart, Chris,Diane, Emilie, and Fred) participated in this study. All of the children were enrolled inspecial education services under the autism category and their cognitive and adaptivefunctioning fell within the moderate intellectual disability range. Specifically, thechildren were selected based on the following criteria: (a) diagnosis of autism or anintellectual disability, (b) an Individual Education Plan (IEP) goal to improve adaptivebehavior related to personal care

Conference Session

Military and Veterans Constituent Committee Division Technical Session 2

Collection

2017 ASEE Annual Conference & Exposition

Authors

Keith A. Landry, Georgia Southern University; N. Mike Jackson, Georgia Southern University; Kevin Gavin Finley, Georgia Southern University - College of Engineering and Information Technology

Tagged Topics

Diversity

Tagged Divisions

Military and Veterans

Theory Perspectives and Veteran Student Barriers/ProblemsSTUDY CHARACTERISTICS: MENTORS & STUDENTSThe authors employed a targeted marketing plan in the Fall 2016 semester to recruit veteranmentors and students for the mentorship program. The Registrar identified 78 veterans serving onthe faculty and staff. The authors approached 10 individuals who were most closely associatedwith CEIT or STEM programs. All 10 volunteered to participate in the mentorship program.In a similar fashion, contact information for all students using GI Bill benefits was made availableto the authors. Email flyers describing the program were sent to each student since they were notcategorized by the type of GI Bill benefit (e.g. Active Duty, Veteran, Dependent, etc

Conference Session

Women in Engineering Division Technical Session 2

Collection

2017 ASEE Annual Conference & Exposition

Authors

Daniela Faas, Franklin W. Olin College of Engineering; Anne M Lucietto, Purdue University, West Lafayette (College of Engineering); Gretchen L. Hein, Michigan Technological University; Lucy Lenhardt, Pennsylvania State University, Erie (Behrend College); Christi Patton Luks, Missouri University of Science & Technology; Beth A Myers, University of Colorado Boulder

Tagged Topics

Diversity

Tagged Divisions

Women in Engineering

participated in volunteer activities throughout the organization.Academics are unique in that their promotion system requires peer evaluated publications in avariety of sources, presentations, dissemination of well-crafted research, and various levels ofrecognition for their work. SWE supports some of the needs of this group, and not others. It isthe authors’ plan to share the survey data with the intent to further develop the understanding ofthis group of members within SWE. It is believed that SWE will enhance their offerings andsupport based upon the findings of this research, while other professional societies review theirprograms and increase their support for a group that has not experienced a great deal of supportin the past. The authors

Conference Session

College Industry Partnerships Division Technical Session 2

Collection

2017 ASEE Annual Conference & Exposition

Authors

Hossein EbrahimNejad, Purdue University

Tagged Divisions

College Industry Partnerships

Sankar, C. S., Kawulich, B., Clayton, H. & Raju, P. K. Developing Leadership Skills in "Introduction to Engineering Courses" through Multi-Media Case Studies. Journal of STEM Education: Innovations and Research 11, 34-60 (2010).23 Davies, J. W. & Rutherford, U. Learning from Fellow Engineering Students Who Have Current Professional Experience. European Journal of Engineering Education 37, 354- 365 (2012).24 Ulijn, J. M., O'Duill, M. & Robertson, S. A. Teaching Business Plan Negotiation: Fostering Entrepreneurship among Business and Engineering Students. Business Communication Quarterly 67, 41-57 (2004).25 Rouvrais, S. s. r. e.-b. f. et al. A mixed project-based learning framework: preparing and

Conference Session

Materials Division Technical Session 3

Collection

2017 ASEE Annual Conference & Exposition

Authors

Linda Vanasupa, California Polytechnic State University, San Luis Obispo; Rishi Kripalani

Tagged Divisions

Materials

fabricate at least 1000 individualbatteries. (A chemical hygiene plan for making these solutions can be downloaded from thedigital commons, http://digitalcommons.calpoly.edu/mate_sop/.)Battery Procedure (See Appendix I for a list of equipment and materials): 1. Layout the design to be printed or email the authors to request their design; 2. Print the layout onto Whatman#1 chromatography paper using a Xerox ColorQube 8580N wax printer; 3. Heat on a hotplate of 150°C for about 60 seconds or hold near a candle flame until the wax has wicked through to the backside of the chromatography paper; 4. Add Al and Ag electrodes with connecting copper tape lines; 5. Dose Technicloth© pads and half-cell regions with 1.7 𝜇L of 1 M AlCl3, 1.7

Conference Session

ETD Green Energy/Sustainability

Collection

2017 ASEE Annual Conference & Exposition

Authors

Regina Ruane Ph.D., Drexel University (Eng. & Eng. Tech.); Richard Chiou, Drexel University (Eng. & Eng. Tech.); Tzu-Liang Bill Tseng, University of Texas, El Paso; Sophia Rose Mayne-DeLuca, Drexel University

Tagged Divisions

Engineering Technology

benefit from the implementation of a solar energy system? Do you foresee any hurdles? Are there any possibilities for expansion beyond your initial plans?Life Cycle Assessment 1. What is a product life cycle and what are its main phases? 2. Describe the four steps in performing life cycle assessment (LCA). 3. How do you achieve the life cycle simulation

Conference Session

Electrical and Computer Division Technical Session 8

Collection

2017 ASEE Annual Conference & Exposition

Authors

Faycal Saffih, University of Waterloo

Tagged Divisions

Electrical and Computer

variousdisciplines in teaching engineering courses is coined as “blended learning” as it blends variousfields in teaching an engineering course and as referenced in [1] at young ages and up to highschool level and beyond!In the present paper, an artificially-intelligent blended learning method is proposed, applied andanalyzed for future recommendation and development. Firstly, the application subject namely thecourse used to implement and carry the suggested approach is presented. In the following section,the suggested pedagogical approach’s plan is laid out and justified to serve the set goals. Finally,and after implementing the proposed holistic pedagogical approach, a quantitative and qualitativeassessment of the suggested blended teaching method is

Conference Session

COED: Gamification and Introducing Students to Programming

Collection

2018 ASEE Annual Conference & Exposition

Authors

Katherine Smith, Old Dominion University; Yuzhong Shen, Old Dominion University; Anthony W. Dean, Old Dominion University

Tagged Divisions

Computers in Education

efficacy of the educationalgame.Future work includes exploration of ways to increase engagement further by incorporatingadditional diegetic elements. For example, in the Element Roll game, the equation generatedcould not only be related to the molecules pictured, but also to the current state of the playerelement. In the Cargo Loading game, steps could be taken to make the flags on the missile morerealistic by having them curved or waving. Special care would have to be taken to ensure that thegraphs were still easy to view. Additionally, we plan to pursue further development of additionalgames for additional topics. It would also be very informative to conduct an efficacy study tocompare the quality of learning outcomes with the level of

Conference Session

Engineering Physics and Physics Division Technical Session 2

Collection

2018 ASEE Annual Conference & Exposition

Authors

Bala Maheswaran, Northeastern University; Cristian Scott Stransky, Northeastern University; Haridas Kumarakuru, Northeastern University

Tagged Divisions

Engineering Physics and Physics

considered its strength, aesthetics, cost, and itsability to support large amounts of copper coils around it.Our main goal is to prove that this model of elevator can generate electricity, and to see if it isprofitable compared to the cost. Since this project was an experiential engineering educationalproject to prove the concept, we did not plan to do further experimentation once the concept isproved, but, we hope that this educational model could lay the groundwork for real worldtechnology development.Methods and ApproachTo build the model, we considered using LEGO bricks, wood, or 3D printed elements. Our firstconcern was practicality, that is, whether the model constructed with a particular material wouldbe suitable to test the concept. Second

Conference Session

Energy Conversion and Conservation Division Best Papers

Collection

2018 ASEE Annual Conference & Exposition

Authors

Jan T. Lugowski, Purdue University, West Lafayette; William Hutzel, Purdue University, West Lafayette

Tagged Divisions

Energy Conversion and Conservation

Foundational (2nd year) Heat Power Fluid Power Applications Applied Applied Electrical 3rd year Thermodynamics Fluid Mechanics Energy Systems Career (4th year) Capstone Co-Op & Internship Electives HVAC Utilities Transportation Manufacturing Figure 1. Energy conversion modules are being integrated into the 4-year plan of study.Integrated Learning In ContextThe green highlighted box in Figure 1 identifies a sophomore-level lab-based thermodynamicscourse that has been re-designed so that students work in small groups on open-ended

Conference Session

Design & Development Projects and Practices

Collection

2018 ASEE Annual Conference & Exposition

Authors

Zhenhua Wu, Virginia State University; Laban K. Rutto; Shahzad Akbar, Virginia State University

Tagged Divisions

Manufacturing

benefit of the local economy.Technologically, the drying process will need to remove about 90% of hop moisture content at arelatively low temperature to maintain hop quality. Under this design objective, alternative cost-effective and sustainable drying technologies were explored for small and medium-sized hop farms.3.2 Scientific design methodTo avoid “design by trial and error”, the well-known scientific design method-quality functiondeployment (QFD), was applied to translate customer needs into measureable designcharacteristics. Customer (grower) needs were captured using discussions, interviews and surveys[5]. This understanding of the customer needs was then summarized in a product planning matrixor ‘house of quality’. These matrices are