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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2023 • Question 4

Question

Math 6310 • Algebra Fall 2023 • Question 4

If some power of a linear map \(A:\mathbb {C}^n\to \mathbb {C}^n\) is the identity (i.e. \(A\) has finite order), show that \(A\) is diagonalizable, i.e. there is a change of basis matrix \(B\) such that \(BAB^{-1}\) is diagonal.

Raw LaTeX

If some power of a linear map \(A:\mathbb{C}^n\to\mathbb{C}^n\) is the identity (i.e. \(A\) has finite order), show that \(A\) is diagonalizable,
i.e. there is a change of basis matrix \(B\) such that \(BAB^{-1}\) is diagonal.

Topic Tags

Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization