Companion factorization in the general linear group \(\mathrm{GL}(n,\mathbb C)\) and applications
Let \(M\) be an \(n\times n\) matrix over the complex numbers. The authors call \(M\) strictly nonsingular if each of its principal submatrices is nonsingular. They prove that each strictly nonsingular matrix \(M\) is a product of \(n\) companion matrices, and give simple expressions for the nonzero entries in the latter matrices in terms of certain subdeterminants of \(M\).
scientific article; zbMATH DE number 5848842
scientific article