K, for every linear map f: EE, for every basis (e₁,...,en), if A is over the basis (e. and if
K, for every linear map f: EE, for every basis (e₁,...,en), if A is over the basis (e. and if
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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Transcribed Image Text:Theorem 7.15. (Cayley-Hamilton) For every finite-dimensional vector space over a field
K, for every linear map f: EE, for every basis (e₁,...,en), if A is the matriz over f
over the basis (e₁,...,en) and if
PA(X) = X + C₁X"¹+...+₂
is the characteristic polynomial of A, then
PA(f) = f +c₁f¹ + ... + cid = 0.
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