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Let T be a linear operator on the finite-dimensional space V. Let c₁,...,Ck be the distinct characteristic values of T and let W; be the space of characteristic vectors associated with the characteristic value c₁. If W = W₁+ . . . + Wk, then dim W= dim W₁ +...+ dim Wk. In fact, if 6₁, is an ordered basis for W₁, then 6 = (6₁, ... ,6) is an orderedbasis for W.

Let T be a linear operator on the finite-dimensional space V. Let c₁,...,Ck be the distinct characteristic values of T and let W; be the space of characteristic vectors associated with the characteristic value c₁. If W = W₁+ . . . + Wk, then dim W= dim W₁ +...+ dim Wk. In fact, if 6₁, is an ordered basis for W₁, then 6 = (6₁, ... ,6) is an orderedbasis for W.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1 Let T be a linear operator on the finite - dimensional space V. Let c₁, . . Ck be the distinct characteristic values of T and let W; be the space of characteristic vectors associated with the characteristic value c¡. If W W₁ + . . . + Wk, then dim W dim W₁ + + dim Wk. = = In fact, if 6₁, is an ordered basis for W₁, then 6 = (6₁, . . . ,6k) is an orderedbasis for W.
Transcribed Image Text:1 Let T be a linear operator on the finite - dimensional space V. Let c₁, . . Ck be the distinct characteristic values of T and let W; be the space of characteristic vectors associated with the characteristic value c¡. If W W₁ + . . . + Wk, then dim W dim W₁ + + dim Wk. = = In fact, if 6₁, is an ordered basis for W₁, then 6 = (6₁, . . . ,6k) is an orderedbasis for W.
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