A determinantal version of the frobenius-konig theorem
Title:
A determinantal version of the frobenius-konig theorem
Author:
Hartfiel, D. J. Loewy, Raphael
Appeared in:
Linear & multilinear algebra
Paging:
Volume 16 (1984) nr. 1-4 pages 155-165
Year:
1984-12
Contents:
Let F be a field and let {d1,…,dk} be a set of independent indeterminates over F. Let A(d1,…,dk) be an n × n matrix each of whose entries is an element of F or a sum of an element of F and one of the indeterminates in {d1,…,dk}. We assume that no d1 appears twice in A(d1,…,dk). We show that if det A(d1,…,dk) = 0 then A(d1,…,dk) must contain an r × s submatrix B, with entries in F, so that r + s = n + p and rank B ≤ p - 1: for some positive integer p.
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