Let A and B be n-square complex matrices with eigenvalues λ₁, λ₂,… λn and μ₁, μ₂,…μn respectively. The matrices A and B are said to have property L if any linear combination aA + bB, with a, b complex, has as eigenvalues the numbers aλᵢ + bμᵢ, i = 1,2, …,n.
A theorem of Dr. M. D. Marcus, which gives a necessary and sufficient condition such that two matrices A and B have property L in terms of the traces of various power-products of A and B, is proved.
This theorem is used to investigate the conditions on B for the special cases n = 2, 3, and 4, when A is in Jordan canonical form.
The final result is a theorem which gives a necessary condition on B for A and B to have property L when A is in Jordan canonical form. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/40177 |
| Date | January 1958 |
| Creators | Chow, Jih-ou |
| 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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