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4) If the linear map T : C → C is diagonalizable and has 1,9 as its only eigenvalues eigenvalues, then its characteristic and minimal polynomials are the same.

4) If the linear map T : C → C is diagonalizable and has 1,9 as its only eigenvalues eigenvalues, then its characteristic and minimal polynomials are the same.

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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4) If the linear map T : C → C³ is diagonalizable and has 1,9 as its only eigenvalues eigenvalues, then its characteristic and minimal polynomials are the same. 5) If SE L(V) is an isometry on the inner product space V, then S - I is always invertible. 6) If N E L(V) is nilpotent then so is I + N². 7) If the product AB of the matrices A € Matm,n(F) and B € Mat,m(F) is non- singular so is the product BA. 8) (2 3 1 = 12. 0 2 3) det 0 0 3 9) Consider R? with its Euclidean inner product. There exists three non-zero vectors in R², which are mutually orthogonal. 10) If A € Mat,, is diagonalizable it admits n linearly independent eigenvectors.
Transcribed Image Text:4) If the linear map T : C → C³ is diagonalizable and has 1,9 as its only eigenvalues eigenvalues, then its characteristic and minimal polynomials are the same. 5) If SE L(V) is an isometry on the inner product space V, then S - I is always invertible. 6) If N E L(V) is nilpotent then so is I + N². 7) If the product AB of the matrices A € Matm,n(F) and B € Mat,m(F) is non- singular so is the product BA. 8) (2 3 1 = 12. 0 2 3) det 0 0 3 9) Consider R? with its Euclidean inner product. There exists three non-zero vectors in R², which are mutually orthogonal. 10) If A € Mat,, is diagonalizable it admits n linearly independent eigenvectors.
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