Affiliation:
1. Shanghai Business School, College of Business and Economics, Shanghai 201400, China
Abstract
Let f(X1,X2,…,Xk) be a matrix function over the field of complex numbers, where X1,X2,…,Xk are a family of matrices with variable entries. The purpose of this paper is to propose and investigate the relationships between certain linear matrix functions that regularly appear in matrix theory and its applications. We shall derive a series of meaningful, necessary, and sufficient conditions for the collections of values of two given matrix functions to be equal through the cogent use of some highly selective formulas and facts regarding ranks, ranges, and generalized inverses of block matrix operations. As applications, we discuss some concrete topics concerning the algebraic connections between general solutions of a given linear matrix equation and its reduced equations.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference22 articles.
1. Ben-Israel, A., and Greville, T.N.E. (2003). Generalized Inverses: Theory and Applications, Springer. [2nd ed.].
2. Bernstein, D.S. (2018). Scalar, Vector, and Matrix Mathematics: Theory, Facts, and Formulas–Revised and Expanded Edition, Princeton University Press.
3. Campbell, S.L., and Meyer, C.D. (2009). Generalized Inverses of Linear Transformations, SIAM.
4. Rao, C.R., and Mitra, S.K. (1971). Generalized Inverse of Matrices and Its Applications, Wiley.
5. Horn, R., and Johnson, C.R. (1991). Topics in Matrix Analysis, Cambridge University Press.
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献