A sufficient condition that a matrix have eigenvalues with non-zero real parts |
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| Authors: | Kenneth J Palmer |
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| Institution: | Department of mathematics , Institute of advanced studies, Australian national university , Canberra, ACT, 2600, Australia |
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| Abstract: | If A is a complex matrix let à be the real matrix obtained by replacing the diagonal elements of A by the moduli of their real parts and by replacing the off-diagonal elements by the negative of their moduli. Then we show that if à is an M-matrix the eigenvalues of A have nonzero real parts and, moreover, the moduli of the real parts are bounded below by the minimum of the real parts of the eigenvalues of Ã. |
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| Keywords: | System of right linear equations Lie nilpotent ring right and left adjoints and determinants |
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