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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Spring 2006 • Question 10

Question

Math 6310 • Algebra Spring 2006 • Question 10

Let \(A\) be a square complex matrix such that \(A^3=A\). Prove that \(A\) is diagonalizable. Is this true over any algebraically closed field?

Raw LaTeX

Let \(A\) be a square complex matrix such that \(A^3=A\). Prove that \(A\) is diagonalizable.
Is this true over any algebraically closed field?

Topic Tags

Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization