Let V be a vector space and let T: V → V be a linear transformation. For each subspace W C V below, verify that W is a T-invariant subspace. (a) W Range(T – I), where I : V → V is the identity. II (b) W = Range(T³), where T" is the n-fold composition T • T . ... • T. (c) W = Null(T + 21).
Let V be a vector space and let T: V → V be a linear transformation. For each subspace W C V below, verify that W is a T-invariant subspace. (a) W Range(T – I), where I : V → V is the identity. II (b) W = Range(T³), where T" is the n-fold composition T • T . ... • T. (c) W = Null(T + 21).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.4: Linear Transformations
Problem 24EQ
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