Suppose that A ∈Mn×n(F) has two distinct eigenvalues, λ1 and λ2, and that dim(Eλ1) = n−1. Prove that A is diagonalizable.
Suppose that A ∈Mn×n(F) has two distinct eigenvalues, λ1 and λ2, and that dim(Eλ1) = n−1. Prove that A is diagonalizable.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.1: Introduction To Eigenvalues And Eigenvectors
Problem 36EQ: Consider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two...
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Suppose that A ∈Mn×n(F) has two distinct eigenvalues, λ1 and λ2, and that dim(Eλ1) = n−1. Prove that A is diagonalizable.
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