منابع مشابه
Neutral subspaces of pairs of symmetric/skewsymmetric real matrices
Let A and B be n × n real matrices with A symmetric and B skewsymmetric. Obviously, every simultaneously neutral subspace for the pair (A,B) is neutral for each Hermitian matrix X of the form X = μA + iλB, where μ and λ are arbitrary real numbers. It is well-known that the dimension of each neutral subspace of X is at most In+(X) + In0(X), and similarly, the dimension of each neutral subspace o...
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Let A and B be n × n real matrices with A symmetric and B skewsymmetric. Obviously, every simultaneously neutral subspace for the pair (A,B) is neutral for each Hermitian matrix X of the form X = μA + iλB, where μ and λ are arbitrary real numbers. It is well-known that the dimension of each neutral subspace of X is at most In+(X) + In0(X), and similarly, the dimension of each neutral subspace o...
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Let $a, b, k,in K$ and $u, v in U(K)$. We show for any idempotent $ein K$, $(a 0|b 0)$ is e-clean iff $(a 0|u(vb + ka) 0)$ is e-clean and if $(a 0|b 0)$ is 0-clean, $(ua 0|u(vb + ka) 0)$ is too.
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The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...
متن کاملe-clean matrices and unit-regular matrices
let a; b; k 2 k and u ; v 2 u(k). we show for any idempotent e 2 k, ( a 0 b 0 ) is e-clean i ( a 0 u(vb + ka) 0 ) is e-clean and if ( a 0 b 0 ) is 0-clean, ( ua 0 u(vb + ka) 0 ) is too.
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ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 2004
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s00229-004-0462-0