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Let T be a linear operator on the space V, and let W, ,W hecessary and sufficient condition that each subspace W,be inva commute 'With each of the projections E,, i.e., TE; = E,T, i = 1,

Let T be a linear operator on the space V, and let W, ,W hecessary and sufficient condition that each subspace W,be inva commute 'With each of the projections E,, i.e., TE; = E,T, i = 1,

Linear Algebra: A Modern Introduction
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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Let T be a linear operator on the space V, and let W,, W and E, , E . Then a ... .... necessary and sufficient condition that each subspace W,be invariant under T is that T commute 'With each of the projections E;, i.e., TE; = E;T, i = 1, ,k
Transcribed Image Text:Let T be a linear operator on the space V, and let W,, W and E, , E . Then a ... .... necessary and sufficient condition that each subspace W,be invariant under T is that T commute 'With each of the projections E;, i.e., TE; = E;T, i = 1, ,k
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