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p = (x – c1)*1 ... (* – 4)", C1 in F

p = (x – c1)*1 ... (* – 4)", C1 in F

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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Let V be a finite – dimensional vector space over the field F. Let T be a linear operator on such that the minimal polynomial for T is a product of linear factors. p = (x – c1)*1 ... ( – 4)*", C1 in F Let W be a proper (W # B) subspace of V which is invariant under T. There exists a vector a in V such that (a) a is not in W; (b) (T – cI)a is in W, for some characteristic value c of the operator T. -
Transcribed Image Text:Let V be a finite – dimensional vector space over the field F. Let T be a linear operator on such that the minimal polynomial for T is a product of linear factors. p = (x – c1)*1 ... ( – 4)*", C1 in F Let W be a proper (W # B) subspace of V which is invariant under T. There exists a vector a in V such that (a) a is not in W; (b) (T – cI)a is in W, for some characteristic value c of the operator T. -
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