FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Common eigenvalues of two matrices |
Kalinina E. A. |
2013, issue 1, P. 52-60 |
Abstract |
| A new approach to determine common eigenvalues of two matrices is proposed. The algorithm is based on the criteria for the existence of common eigenvalues of matrices in the form of algebraic equation depending on their elements and on the properties of solutions of the matrix equation $AX=XB$. The method for constructing a polynomial whose roots equal to the common eigenvalues of matrices $A$ and $B$ is presented. |
Keywords: common eigenvalues of two matrices, Kronecker product |
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References |
| [1] M. Bokher, Vvedenie v vysshuiu algebru, GTTI, M.-L., 1933. [2] E. Dzhuri, Innory i ustoichivost' dinamicheskikh sistem, Nauka, M., 1979. [3] E. A. Kalinina, A.Iu. Uteshev, Teoriia iskliucheniia. Ucheb. posobie, NII Khimii SPb-GU, SPb., 2002. [4] C. C. MacDuffee, The Theory of Matrices, Chelsea Publishing Company, N.-Y., 1956. [5] K. Datta, “An algorithm to determine if two matrices have common eigenvalues”, IEEE Transactions on Automatic Control, 27:5 (1982), 1131–1133. [6] T. D. Roopamala, S. K. Katti, “New Approach to Identify Common Eigenvalues of real matrices using Gerschgorin Theorem and Bisection method”, (IJCSIS) International Journal of Computer Science and Information Security, 7:2 (2010). [7] F.R. Gantmakher, Teoriia matrits, Nauka, M., 1967. |