The solution of the Binet-Cauchy functional equation for square matrices

✍ Scribed by Konrad J. Heuvers; Daniel S. Moak

• Publisher: Elsevier Science
• Year: 1991
• Tongue: English
• Weight: 609 KB
• Volume: 88
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(91)90056-8

✦ Synopsis

Heuvers, K.J. and D.S. Moak, The solution of the Binet-Cauchy functional equation for square matrices, Discrete Mathematics 88 (1991) 21-32. It is shown that if f : M,(K)+ K is a nonconstant solution of the Binet-Cauchy functional equation for A, B E M,,(K) and if f(E) = 0 where E is the n x n matrix with all entries l/n then f is given by f(A) = m(det A) where m is a multiplicative function on K. For f(E) # 0 it has been shown by Heuvers, Cummings and Bhaskara Rao, that f(A) = @(per A) where 9 is an isomorphism of K. Thus the Binet-Cauchy functional equation is the source of the common properties of det A and per A. The value of f(E) is sufficient to distinguish between the two functions.