A Polynomial Approach to Linear Algebra by Paul A. Fuhrmann

Author:Paul A. Fuhrmann
Language: eng
Format: epub, pdf
Publisher: Springer New York, New York, NY

where D = diag (σ1, …, σ r ). Compare with Theorem 7.58.

18.Show that the eigenvalues of are .

7.7 Notes and Remarks

Most of the results in this chapter go over in one way or another to the context of Hilbert spaces, where, in fact, most of them were proved initially. Young (1988) is a good, very readable modern source for the basics of Hilbert space theory.

The spectral theorem in Hilbert space was one of the major early achievements of functional analysis and operator theory. For an extensive source on these topics and the history of the subject, see Dunford and Schwartz (1958, 1963).

Singular values were introduced by E. Schmidt in 1907. Because of the importance of singular values as approximation numbers, equation (7.22) is sometimes taken as the definition of singular values. In this connection, see Young (1988).

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.