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UBC Theses and Dissertations
Pairs of matrices with property L. Chow, Jih-ou
Abstract
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.
Item Metadata
| Title |
Pairs of matrices with property L.
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| Creator | |
| Publisher |
University of British Columbia
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| Date Issued |
1958
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| Description |
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.
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| Genre | |
| Type | |
| Language |
eng
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| Date Available |
2012-01-19
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| Provider |
Vancouver : University of British Columbia Library
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| 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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| DOI |
10.14288/1.0080642
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| URI | |
| Degree (Theses) | |
| Program (Theses) | |
| Affiliation | |
| Degree Grantor |
University of British Columbia
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| Campus | |
| Scholarly Level |
Graduate
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| Aggregated Source Repository |
DSpace
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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.