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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1998 • Question 2

Question

Math 6310 • Algebra Fall 1998 • Question 2

Let \(M\) be a square matrix over \(\mathbb {C}\) such that \(M^k\) is the identity matrix for some integer \(k>0\). Show that \(M\) is diagonalizable.

Raw LaTeX

Let \(M\) be a square matrix over \(\mathbb{C}\) such that \(M^k\) is the identity matrix for some
integer \(k>0\). Show that \(M\) is diagonalizable.

Topic Tags

Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization