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- Let T€ B(H). (a) Show that ker T'T=ker T. (b) Show that TT and TT have the same eigenvalues. (c) Give an example of T with TT TT¹.

- Let T€ B(H). (a) Show that ker T'T=ker T. (b) Show that TT and TT have the same eigenvalues. (c) Give an example of T with TT TT¹.

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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11. Let TE B(H). (a) Show that ker T'T = ker T. (b) Show that T'T and TT' have the same eigenvalues. (c) Give an example of T with T'T # TT'.
Transcribed Image Text:11. Let TE B(H). (a) Show that ker T'T = ker T. (b) Show that T'T and TT' have the same eigenvalues. (c) Give an example of T with T'T # TT'.
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