Question

A square matrix A is said to be idempotent if A2 = A. Let A be an idempotent matrix.

Answer 1

Answer:

An n × n matrix is said to be idempotent if A2 = A. Show that if λ is an eigenvalue of an idempotent matrix then λ must be either 0 or 1. By the definiton of an eigenvalue we know from the given that there is a nonzero vector x such that Ax = λx. ... This then clearly implies that λ = 0, 1.