2. Let T be a linear operator on V. Suppose V = W1 eW2, where the subspaces W1 and W2 are invariant under T. Let T; be the induced (restriction) operator on Wi, i = 1, 2. Prove that characteristic polynomial for T is the product of the characteristic polynomials for T1, T2.
2. Let T be a linear operator on V. Suppose V = W1 eW2, where the subspaces W1 and W2 are invariant under T. Let T; be the induced (restriction) operator on Wi, i = 1, 2. Prove that characteristic polynomial for T is the product of the characteristic polynomials for T1, T2.
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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