منابع مشابه
Bounded Groups and Norm - Hermitian Matrices 9
and Hans Schneider· Department of Mathematics University of Wisconsin Madison, Wisconsin 53706 An elementary proof is given that a bounded multiplicative group of complex (real) n X n nonsingular matrices is similar to a unitary (orthogonal) group. Given a norm on a complex n-space, it follows that there exists a nonsingular n X n matrix L (the lAewner-John matrix for the norm) such that LHL -1...
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If v is a norm on en, let H(v) denote the set of all norm-Hermitians in e nn. Let S be a subset of the set of real diagonal matrices D. Then there exists a norm v such that S = H(v) (or S = H(v) n D) if and only if S contains the identity and S is a subspace of D with a basis consisting of rational vectors. As a corollary, it is shown that, for a diagonable matrix h with distinct eigenvalues .1...
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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 ...
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Let v be a (standardized) absolute norm on en. A matrix H in enn is called normHermitian jf the numerical range V(H) determined by v is real. Let :re be the set of all norm-Hermitians in en"' We determine an equivalence relation'" on {t, .•. , n} with the following property: Let HE en"' Then HE :re if and only if H is Hermitian and h,) = 0 if i + j. Let,l =.# + i:lC. Then.l is a subalgebra of e...
متن کاملCongruence of Hermitian Matrices by Hermitian Matrices
Two Hermitian matrices A, B ∈ Mn(C) are said to be Hermitian-congruent if there exists a nonsingular Hermitian matrix C ∈ Mn(C) such that B = CAC. In this paper, we give necessary and sufficient conditions for two nonsingular simultaneously unitarily diagonalizable Hermitian matrices A and B to be Hermitian-congruent. Moreover, when A and B are Hermitian-congruent, we describe the possible iner...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1974
ISSN: 0024-3795
DOI: 10.1016/0024-3795(74)90022-6