(3) Suppose that V is a finite dimensional vector space over R and T € L(V) has no eigenvalues. Prove that every T-invariant subspace of V has even dimension.
(3) Suppose that V is a finite dimensional vector space over R and T € L(V) has no eigenvalues. Prove that every T-invariant subspace of V has even dimension.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 43EQ
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