{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T12:53:51Z","timestamp":1743080031361,"version":"3.40.3"},"publisher-location":"Cham","reference-count":21,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031427527"},{"type":"electronic","value":"9783031427534"}],"license":[{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2023,1,1]],"date-time":"2023-01-01T00:00:00Z","timestamp":1672531200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023]]},"DOI":"10.1007\/978-3-031-42753-4_8","type":"book-chapter","created":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T06:02:35Z","timestamp":1693375355000},"page":"113-129","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Teaching Linear Algebra in\u00a0a\u00a0Mechanized Mathematical Environment"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0515-1572","authenticated-orcid":false,"given":"Robert M.","family":"Corless","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2161-6803","authenticated-orcid":false,"given":"David J.","family":"Jeffrey","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0009-0003-6181-4665","authenticated-orcid":false,"given":"Azar","family":"Shakoori","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2023,8,28]]},"reference":[{"key":"8_CR1","unstructured":"Banks, J., Garza-Vargas, J., Srivastava, N.: Global convergence of Hessenberg shifted QR I: Dynamics (2022)"},{"key":"8_CR2","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/978-3-030-86909-0_12","volume-title":"Mathematics Education in the Age of Artificial Intelligence","author":"J Betteridge","year":"2022","unstructured":"Betteridge, J., Chan, E.Y.S., Corless, R.M., Davenport, J.H., Grant, J.: Teaching programming for mathematical scientists. In: Richard, P.R., V\u00e9lez, M.P., Van Vaerenbergh, S. (eds.) Mathematics Education in the Age of Artificial Intelligence, vol. 17, pp. 251\u2013276. Springer, Cham (2022). https:\/\/doi.org\/10.1007\/978-3-030-86909-0_12"},{"issue":"1","key":"8_CR3","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1145\/382276.1095228","volume":"24","author":"B Buchberger","year":"1990","unstructured":"Buchberger, B.: Should students learn integration rules? ACM SIGSAM Bull. 24(1), 10\u201317 (1990)","journal-title":"ACM SIGSAM Bull."},{"key":"8_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1007\/978-3-030-43120-4_8","volume-title":"Mathematical Aspects of Computer and Information Sciences","author":"AC Camargos Couto","year":"2020","unstructured":"Camargos Couto, A.C., Moreno Maza, M., Linder, D., Jeffrey, D.J., Corless, R.M.: Comprehensive LU factors of polynomial matrices. In: Slamanig, D., Tsigaridas, E., Zafeirakopoulos, Z. (eds.) MACIS 2019. LNCS, vol. 11989, pp. 80\u201388. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-43120-4_8"},{"issue":"4","key":"8_CR5","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1080\/07468342.1992.11973473","volume":"23","author":"D Carlson","year":"1992","unstructured":"Carlson, D., Johnson, C.R., Lay, D., Porter, A.D.: Gems of exposition in elementary linear algebra. Coll. Math. J. 23(4), 299\u2013303 (1992). https:\/\/doi.org\/10.1080\/07468342.1992.11973473","journal-title":"Coll. Math. J."},{"issue":"1","key":"8_CR6","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1080\/07468342.1993.11973504","volume":"24","author":"D Carlson","year":"1993","unstructured":"Carlson, D., Johnson, C.R., Lay, D.C., Porter, A.D.: The linear algebra curriculum study group recommendations for the first course in linear algebra. Coll. Math. J. 24(1), 41\u201346 (1993)","journal-title":"Coll. Math. J."},{"key":"8_CR7","doi-asserted-by":"publisher","first-page":"41","DOI":"10.1007\/s11786-018-0364-2","volume":"13","author":"EY Chan","year":"2019","unstructured":"Chan, E.Y., Corless, R.M.: Minimal height companion matrices for Euclid polynomials. Math. Comput. Sci. 13, 41\u201356 (2019)","journal-title":"Math. Comput. Sci."},{"key":"8_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"188","DOI":"10.1007\/978-3-030-60026-6_11","volume-title":"Computer Algebra in Scientific Computing","author":"RM Corless","year":"2020","unstructured":"Corless, R.M., Giesbrecht, M., Rafiee Sevyeri, L., Saunders, B.D.: On parametric linear system solving. In: Boulier, F., England, M., Sadykov, T.M., Vorozhtsov, E.V. (eds.) CASC 2020. LNCS, vol. 12291, pp. 188\u2013205. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-60026-6_11"},{"issue":"3","key":"8_CR9","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1145\/271130.271135","volume":"31","author":"RM Corless","year":"1997","unstructured":"Corless, R.M., Jeffrey, D.J.: The Turing factorization of a rectangular matrix. ACM SIGSAM Bull. 31(3), 20\u201330 (1997)","journal-title":"ACM SIGSAM Bull."},{"key":"8_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1007\/978-3-319-72453-9_13","volume-title":"Mathematical Aspects of Computer and Information Sciences","author":"RM Corless","year":"2017","unstructured":"Corless, R.M., Moreno Maza, M., Thornton, S.E.: Jordan canonical form with parameters from Frobenius form\u00a0with parameters. In: Bl\u00f6mer, J., Kotsireas, I.S., Kutsia, T., Simos, D.E. (eds.) MACIS 2017. LNCS, vol. 10693, pp. 179\u2013194. Springer, Cham (2017). https:\/\/doi.org\/10.1007\/978-3-319-72453-9_13"},{"key":"8_CR11","doi-asserted-by":"crossref","unstructured":"Deng, S., Reid, G., Jeffrey, D.: Parametric linear algebra in maple: reduced row echelon form. In: Proceedings of SYNASC, pp. 33\u201336. IEEE (2021)","DOI":"10.1109\/SYNASC54541.2021.00017"},{"key":"8_CR12","doi-asserted-by":"crossref","unstructured":"Higham, N.J.: Accuracy and Stability of Numerical Algorithms, 2nd edn. SIAM, Philadelphia (2002)","DOI":"10.1137\/1.9780898718027"},{"key":"8_CR13","doi-asserted-by":"crossref","unstructured":"Jeffrey, D.J., Corless, R.M.: Linear algebra in maple\u00ae. In: Hogben, L. (ed.) Handbook of Linear Algebra, 2nd edn., pp. 89\u20131. Chapman and Hall\/CRC, Boca Raton (2013)","DOI":"10.1201\/b16113-110"},{"key":"8_CR14","unstructured":"Lay, D.C., Lay, S.R., McDonald, J.: Linear Algebra and Its Applications. Pearson Education, New York (2016)"},{"key":"8_CR15","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1016\/0024-3795(95)00257-X","volume":"241","author":"V Mehrmann","year":"1996","unstructured":"Mehrmann, V.: A step toward a unified treatment of continuous and discrete time control problems. Linear Algebra Appl. 241, 749\u2013779 (1996)","journal-title":"Linear Algebra Appl."},{"key":"8_CR16","unstructured":"Moler, C.: Roots\u2013of polynomials, that is (1991). https:\/\/www.mathworks.com\/company\/newsletters\/articles\/roots-of-polynomials-that-is.html"},{"key":"8_CR17","doi-asserted-by":"publisher","unstructured":"Sexton, A., Sorge, V.: Abstract matrices in symbolic computation. In: Proceedings of ISSAC. ACM, July 2006. https:\/\/doi.org\/10.1145\/1145768.1145820","DOI":"10.1145\/1145768.1145820"},{"key":"8_CR18","doi-asserted-by":"crossref","unstructured":"Sexton, A.P., Sorge, V., Watt, S.M.: Computing with abstract matrix structures. In: Proceedings of ISSAC, pp. 325\u2013332 (2009)","DOI":"10.1145\/1576702.1576747"},{"issue":"4","key":"8_CR19","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1016\/S0747-7171(08)80104-6","volume":"13","author":"WY Sit","year":"1992","unstructured":"Sit, W.Y.: An algorithm for solving parametric linear systems. J. Symb. Comput. 13(4), 353\u2013394 (1992)","journal-title":"J. Symb. Comput."},{"key":"8_CR20","volume-title":"Introduction to Applied Mathematics","author":"G Strang","year":"1986","unstructured":"Strang, G.: Introduction to Applied Mathematics. Wellesley-Cambridge Press, Wellesley (1986)"},{"key":"8_CR21","doi-asserted-by":"crossref","unstructured":"Van Loan, C.F., Fan, K.Y.D.: Insight Through Computing - A MATLAB Introduction to Computational Science and Engineering. SIAM, Philadelphia (2010)","DOI":"10.1137\/1.9780898717648"}],"container-title":["Lecture Notes in Computer Science","Intelligent Computer Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-42753-4_8","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T06:03:37Z","timestamp":1693375417000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-42753-4_8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023]]},"ISBN":["9783031427527","9783031427534"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-42753-4_8","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2023]]},"assertion":[{"value":"28 August 2023","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CICM","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Intelligent Computer Mathematics","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Cambridge","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"United Kingdom","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2023","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"4 September 2023","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"8 September 2023","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"16","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"mkm2023","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/cicm-conference.org\/2023\/cicm.php","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"31","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"16","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"6","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"52% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}