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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2005 • Question 9

Question

Math 6310 • Algebra Fall 2005 • Question 9

Let \(A\) be an \(n\times n\) matrix with complex coefficients. Show that \(A^n=0\) if and only if \(\operatorname {tr}(A^i)=0\) for all \(i>0\).

Raw LaTeX

Let \(A\) be an \(n\times n\) matrix with complex coefficients. Show that \(A^n=0\) if and only if
\(\operatorname{tr}(A^i)=0\) for all \(i>0\).

Topic Tags

Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization