Title

The Binet-Cauchy Functional Equation and Nonsingular Multiindexed Matrices

Authors

Konrad J. Heuvers, Michigan Technological University
Daniel S. Moak, Michigan Technological University

Document Type

Article

Publication Date

10-15-1990

Department

Department of Mathematical Sciences

Abstract

In a first theorem it is shown that a multiindexed matrix M = (M_σ,τ) is nonsingular where M_σ,τ is a multivariate polynomial in q-tuples of nonnegative integers σ and τ. In a second theorem a uniqueness relation of multinomial type is established. Finally, it is shown that, up to isomorphism, a nonzero function f:M_n(K)→K must be the determinant function if f(E) = 0, where E is the n × n matrix with all entries 1n, and f satisfies the Binet-Cauchy function equation

f(AB) = 1n!∑|s| = nnsf(A^s)f(B_s)

for square matrices A, B∈M_n(K) and for rectangular matrices A∈M_n×(n+1)(K) and B∈M_(n+1)×n(K).

Publisher's Statement

© 1990

Publication Title

Linear Algebra and Its Applications

Recommended Citation

Heuvers, K., & Moak, D. (1990). The Binet-Cauchy Functional Equation and Nonsingular Multiindexed Matrices. Linear Algebra and Its Applications, 140, 197-215. http://doi.org/10.1016/0024-3795(90)90230-A
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5395