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linear operator on the finite – dimensional space V. Let c1,...,Cg be the distinct characteristic values o charactorictio Toctors associatod writh the charactorictic value . TE W W. thon

linear operator on the finite – dimensional space V. Let c1,...,Cg be the distinct characteristic values o charactorictio Toctors associatod writh the charactorictic value . TE W W. thon

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 33EQ
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Let T be a linear operator on the finite – dimensional space V. Let c1, . . ,Cx be the distinct characteristic values of T and let W; be the space of characteristic vectors associated with the characteristic value c;. If W = W, + . . . +Wk, then dim W dim W, + . . .+ dim Wk. In fact, if 6;, is an ordered basis for Wi, then 6 = (61, . .. ,6k) is an orderedbasis for W.
Transcribed Image Text:Let T be a linear operator on the finite – dimensional space V. Let c1, . . ,Cx be the distinct characteristic values of T and let W; be the space of characteristic vectors associated with the characteristic value c;. If W = W, + . . . +Wk, then dim W dim W, + . . .+ dim Wk. In fact, if 6;, is an ordered basis for Wi, then 6 = (61, . .. ,6k) is an orderedbasis for W.
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