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If T₁ is the restriction of T to W₁ and T2 is the restriction of T to W₂, where, T:V→V is a linear operator and p(x) = f(x) g(x) such that p(x) is the minimal polynomial of T and f(x) and g(x) are monic. Then f(x) and g(x) are minimal polynomials of T₁ and T2 caonactively

If T₁ is the restriction of T to W₁ and T2 is the restriction of T to W₂, where, T:V→V is a linear operator and p(x) = f(x) g(x) such that p(x) is the minimal polynomial of T and f(x) and g(x) are monic. Then f(x) and g(x) are minimal polynomials of T₁ and T2 caonactively

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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Que 124: If T, is the restriction of T to W₁ and T₂ is the restriction of T to W₂, where, T: V→ V is a linear operator and p(x) = f(x) g(x) such that p(x) is the minimal polynomial of T and f(x) and g(x) are monic. Then f(x) and g(x) are minimal polynomials of T₁ and T₂ respectively.
Transcribed Image Text:Que 124: If T, is the restriction of T to W₁ and T₂ is the restriction of T to W₂, where, T: V→ V is a linear operator and p(x) = f(x) g(x) such that p(x) is the minimal polynomial of T and f(x) and g(x) are monic. Then f(x) and g(x) are minimal polynomials of T₁ and T₂ respectively.
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