全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...

What the Volume of Matrices Says?

DOI: 10.4236/alamt.2020.104005, PP. 53-69

Keywords: Matrices, Matrix Addition, Matrix Subtraction, Matrix Division, Dividend Matrix, Divisor Matrix, Quotient Matrix, Remainder Matrix, Fraction Division

Full-Text   Cite this paper   Add to My Lib

Abstract:

We know matrices and their transposes and we also know flip matrices. In my previous paper Matrices-One Review, I introduced transprocal matrix. Flip matrices are transpose of transprocal matrices. Now I would like to introduce water image of four matrices said above and properties of such matrices. Also we know, determinant of sum of matrices is not equal to sum of determinant of matrices. Why can’t we get equal value on addition side and additive side of determinant of matrix addition and subtraction? This question triggered me to find the reason. The basic algebra of mensuration gave ideas to retreat determinant of matrix addition and subtraction. I extent that ideas for matrices sum. Further, in 1812, French mathematician Jacques Philippe Marie Binet described how to multiply matrices. Matrices are defined on addition, subtraction and multiplication but not in division. By the inspiration of Binet, I would like to describe how to do divisions on matrices. This idea is derived from division of fractions. In division of fraction, reciprocal of divisor fraction multiplies with dividend fraction. I do the same in division on matrices with some modifications. By this way, we could find quotient matrix and remainder matrix which satisfy division algorithm. So we could say, determinant of division of dividend matrix and divisor matrix is equal to division of determinant of dividend matrix and determinant of divisor matrix.

References

[1]  Wikipedia.
http://en.wikipedia.org/wiki/Matrix_
[2]  Lipschuts, S. and Lipson, M.L. (2011) Theory and Problems of Linear Algebra. 3rd Edition, Tata McGraw-Hill, India.
[3]  Rangasamy, B.P. (2019) Matrices—One Review. Advances in Linear Algebra & Matrix Theory, 9, 43-72.
https://doi.org/10.4236/alamt.2019.93004
[4]  Rangasamy, B.P. (2020) One Approach to Matrix. International Journal of Innovative Studies in Sciences and Engineering Technology, 6, 38-45.
https://ijisset.org/

Full-Text

comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133

WeChat 1538708413