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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2008 • Question 6

Question

Math 6310 • Algebra Fall 2008 • Question 6

A square matrix \(M\) is idempotent if \(M^2=M\). Prove that two idempotent \(n\times n\) matrices over a field are similar if and only if they have the same rank.

Raw LaTeX

A square matrix \(M\) is idempotent if \(M^2=M\). Prove that two idempotent \(n\times n\)
matrices over a field are similar if and only if they have the same rank.

Topic Tags

Matrix Similarity, Jordan Forms, and Finite-Order Diagonalization