A characterization of the permanent function by the Binet-Cauchy theorem
β Scribed by Konrad J. Heuvers; L.J. Cummings; K.P.S. Bhaskara Rao
- Book ID
- 107825226
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 884 KB
- Volume
- 101
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let A, B be multi-dimensional matrices of boundary format p i=0 (k i + 1), q j =0 (l j + 1), respectively. Assume that k p = l 0 so that the convolution A \* B is defined. We prove that Det(A \* B) = Det(A) Ξ± β’ Det(B) Ξ² where Ξ± = l 0 !/(l 1 ! . . . l q !), Ξ² = (k 0 + 1)!/(k 1 ! . . . k p-1 !(k p + 1
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 matri