9) Suppose V is finite-dimensional and T E L(V). Let 11, ..., Am denote the distinct nonzero eigenvalues of T. Prove that dim E (11,T)+ …+ dim E (Am , T') < dim (range T') ...

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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9
eigenvectors as 1 (not hecessarily
same eigenvalues). Pro
ST = TS.
9) Suppose V is finite-dimensional and T e L(V). Let d,..., am denote the distinct nonzero
eigenvalues of T. Prove that dim E(2, , T) + …· + dim E (Am ,T)< dim (range T)
10) Define T E L(R²) by T(x. v) = (41x + 7v. -20x + 74v), Verify that the matrix of T
Transcribed Image Text:eigenvectors as 1 (not hecessarily same eigenvalues). Pro ST = TS. 9) Suppose V is finite-dimensional and T e L(V). Let d,..., am denote the distinct nonzero eigenvalues of T. Prove that dim E(2, , T) + …· + dim E (Am ,T)< dim (range T) 10) Define T E L(R²) by T(x. v) = (41x + 7v. -20x + 74v), Verify that the matrix of T
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