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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2008 • Question 4

Question

Math 6310 • Algebra Fall 2008 • Question 4

Let \(M\) be an element of \(GL_n(\mathbb {C})\) that has finite order. Is \(M\) necessarily diagonalizable? Prove or disprove.

Raw LaTeX

Let \(M\) be an element of \(GL_n(\mathbb{C})\) that has finite order. Is \(M\) necessarily
diagonalizable? Prove or disprove.

Topic Tags

Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization