Matricial logarithmic derivatives |
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Authors: | Emeric Deutsch Max Mlynarski |
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Affiliation: | Deparment of Mathematics Polytechnic Institute of New York Brooklyn, New York 11201, USA;Department of Mathematics Kingsborough Community College Brooklyn, New York 11235, USA |
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Abstract: | If θ is a norm on Cn, then the mapping from Mn(C) (=Cn × n) into R is called the logarithmic derivative induced by the vector norm θ. In this paper we generalize this concept to a mapping γ from Mn(C) into Mk(R), where k ? n. Denoting by α(B) the spectral abscissa of a square matrix B (the largest of the real parts of the eigenvalues), we show, in particular, that α(A) ?α(γ(A)). As a byproduct we obtain simple sufficient conditions for the stability of a matrix. |
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