- 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.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter5: Orthogonality
Section5.3: The Gram-schmidt Process And The Qr Factorization
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t is an operator
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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