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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2016 • Question 4

Question

Math 6310 • Algebra Spring 2016 • Question 4

Prove that \(n\times n\) matrices \(A\) and \(B\) have the same characteristic polynomial if and only if the trace of \(A^k\) equals the trace of \(B^k\) for each \(k\ge 1\).

Raw LaTeX

Prove that \(n\times n\) matrices \(A\) and \(B\) have the same characteristic polynomial if and
only if the trace of \(A^k\) equals the trace of \(B^k\) for each \(k\ge 1\).

Topic Tags

Galois Groups of Polynomials Irreducible Polynomials Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization Polynomial Rings and Ring Homomorphism Kernels