If A is an n-square matrix, the p-th compound of A is a matrix whose entries are the p-th order minors of A arranged in a doubly lexicographic order . In this thesis some of the theory of compound matrices is given, including a short proof of the Sylvester-Franke theorem. This theory is used to obtain an extremum property of elementary symmetric functions of the k largest (or smallest) eigenvalues of non-negative Hermitian (n.n.h) matrices. Extensions of theorems due to Weyl and Wielandt are given. The first of these relates elementary symmetric functions of singular values of any matrix A with the same elementary symmetric functions of the eigenvalues. The second gives an extremum property of arbitrary eigenvalues of n.n.h matrices and enables inequalities relating the eigenvalues of A, B with the eigenvalues of A + B to be given (A, B, n.n.h.). Finally, a norm inequality for an arbitrary matrix is given. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/40586 |
| Date | January 1956 |
| Creators | Thompson, Robert Charles |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
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