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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2010 • Question 5

Question

Math 6310 • Algebra Fall 2010 • Question 5

Recall that a Hermitian matrix is a complex matrix which equals its conjugate transpose. Determine the conjugacy classes of \(5\times 5\) Hermitian matrices \(A\) satisfying \(A^5+2A^3+3A=6I\).

Raw LaTeX

Recall that a Hermitian matrix is a complex matrix which equals its conjugate transpose.
Determine the conjugacy classes of \(5\times 5\) Hermitian matrices \(A\) satisfying
\(A^5+2A^3+3A=6I\).

Topic Tags

Finite Group Theory Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization