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Questions about the determinant of square matrices or linear endomorphisms. Also for closely related topics such as minors or regularized determinants.

2 votes
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192 views

$\det(I+A) \leq 1$ with equality if and only if $A$ is nilpotent

Suppose we are given the following: An $n \times n$ matrix $A$ (with rational entries). $\operatorname{trace}(A)=0$ $B=A+I$ where $I$ is the $n \times n$ identity matrix. Question. What condition …