Yahoo Answers: Answers and Comments for Linear Algebra eigenvalue proof question? [Mathematics]
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enCA
Wed, 27 Nov 2013 18:43:27 +0000
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Yahoo Answers: Answers and Comments for Linear Algebra eigenvalue proof question? [Mathematics]
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https://ca.answers.yahoo.com/question/index?qid=20131127184327AAQqtOk
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From Eugene: Write f(t) = ∑(i = 0, k) c_i t^i Since Av = λ...
https://ca.answers.yahoo.com/question/index?qid=20131127184327AAQqtOk
https://ca.answers.yahoo.com/question/index?qid=20131127184327AAQqtOk
Wed, 27 Nov 2013 18:58:35 +0000
Write f(t) = ∑(i = 0, k) c_i t^i Since Av = λv,
A^i(v) = A^(i1)(Av) = λA^(i1)v = ••• = λ^(i1)Av = λ^i(v)
for all i ≥ 1. Therefore
f(A)v = ∑(i = 0, k) c_i A^i(v) = ∑(i = 0, k) c_i λ^i(v) = f(λ)v.