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If W is an invariant subspace for T then W is invariant under every polynomial in T

If W is an invariant subspace for T then W is invariant under every polynomial in T

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.1: Vector Spaces And Subspaces
Problem 37EQ: In Exercises 24-45, use Theorem 6.2 to determine whether W is a subspace of V. 37. V = P, W is the...
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If W is an invariant subspace for T , then W is invariant under every polynomial in T Thus , for each a in V , the conductor S (a; W) is an ideal in the polynomial algebra F [x] .
Transcribed Image Text:If W is an invariant subspace for T , then W is invariant under every polynomial in T Thus , for each a in V , the conductor S (a; W) is an ideal in the polynomial algebra F [x] .
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