Math Forum :: View topic – Calc + linear Algebra

First, note that if has an eigenvalue which is an odd integer, then the matrix , which is singular, is a matrix with odd integers in diagonal entries but even integers in other entries. When we expand using (something like that), it is easily seen that there is only one odd term in the expansion, namely the product of the diagonal entries. Hence should be odd but due to the singularity of . Contradiction holds.[/tex][/dollar]