[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.7468/jksmee.2012.26.4.351

Early History of Linear Algebra 초기 선형대수학의 역사

Lee, Sang-Gu (Department of Mathematics, Sungkyunkwan University)
Lee, Jae Hwa (BK21 Math. Modeling HRD Division, Sungkyunkwan University)
Ham, Yoon Mee (Department of Mathematics, Kyonggi University)

Publication Information

Communications of Mathematical Education / v.26, no.4, 2012 , pp. 351-362 More about this Journal

Abstract

Until the 1950s, linear algebra was considered only as one of abstract and advanced mathematics subject among in graduate mathematics courses, mainly dealing with module in algebra. Since the 1960s, it has been a main subject in undergraduate mathematics education because matrices has been used all over. In Korea, it was considered as a course only for mathematics major students until 1980s. However, now it is a subject for all undergraduate students including natural science, engineering, social science since 1990s. In this paper, we investigate the early history of linear algebra and its development from a historical perspective and mathematicians who made contributions. Secondly, we explain why linear algebra became so popular in college mathematics education in the late 20th century. Contributions of Chinese and H. Grassmann will be extensively examined with many newly discovered facts.

Keywords

Babylonia; JiuZhangSuanShu: The Nine Chapters on the Mathematical Art; Seki Kowa; Leibniz; M $\ddot{o}$ bius; Grassmann; Hankel; Klein; Cauchy; Determinant; Sylvester; Matrices; Linear Algebra; Cayley; Matrix algebra; Bourbaki; Gantmacher; LP; RSA-code; Google matrix; textbook; education;

Citations & Related Records

Reference

1	이상구․강옥기 (1997). 행렬이론의 발전과정과 현재, 대한수학회 뉴스레터, 55, 20-27.
2	이상구․함윤미 (2006). 실베스터와 클라인 그리고 19세기 미국 수학, 한국수학사학회지, 19(2), 77-88.
3	Benzi, M. (2009). The Early History of Matrix Iterations: with a Focus on the Italian Contribution, presented at the SIAM Conference on Applied Linear Algebra, Monterey, California. http://www.siam.org/meetings/la09/talks/benzi.pdf
4	Carlson, D., Johnson, C. R., Lay, D. C., and Porter, A. D. (1993). The Linear Algebra Curriculum Study Group Recommendations for the First Course in Linear Algebra, The College Mathematics Journal , 24(1), 41-46. DOI ScienceOn
5	Crowe, J. (1967). A History of Vector Analysis: The Evolution of the Idea of a Vectorial System, University of Notre Dame Press.
6	Crilly, T. (2006). Arthur Cayley: Mathematician Laureate of the Victorian Age, The Johns Hopkins University Press.
7	Dorier, J. (1995). A General Outline of the Genesis of Vector Space Theory, Historia Mathematica, 22, 227-261. DOI ScienceOn
8	Fearnley-Sander, D. (1979). Hermann Grassmann and the creation of linear algebra, The American Mathematical Monthly, 86(10), 809-817. DOI ScienceOn
9	Frazer, R. A., Duncan, W. J., and Collar, A. R. (1938). Elementary Matrices and Some Applications to Dynamics and Differential Equations, 10th ed., Cambridge University Press.
10	Hart, R. (2010). The Chinese Roots of Linear Algebra, Johns Hopkins University Press.
11	Higham, N. (2009). Cayley, Sylvester, and Early Matrix Theory, presented at the SIAM Conference on Applied Linear Algebra, Monterey, California. http://www.siam.org/meetings/la09/talks/higham.pdf
12	Horn, R., Johnson C. (1990), Matrix Analysis, Cambridge University Press.
13	Parshall, K. H. (2006). James Joseph Sylvester. Jewish Mathematician in a Victorian World, The Johns Hopkins University Press.
14	Sylvester, J. J. (1851). Explanation of the coincidence of a theorem given by Mr Sylvester in the December number of this journal, with one stated by Professor Donkin in the June number of the same, Philosophical Magazine, 4th Series 1, 44-46.