منابع مشابه
Majorization Bounds for Ritz Values of Hermitian Matrices∗
Given an approximate invariant subspace we discuss the effectiveness of majorization bounds for assessing the accuracy of the resulting Rayleigh-Ritz approximations to eigenvalues of Hermitian matrices. We derive a slightly stronger result than previously for the approximation of k extreme eigenvalues, and examine some advantages of these majorization bounds compared with classical bounds. From...
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Let A ⊆ Mn(C) be a unital ∗-subalgebra of the algebra Mn(C) of all n × n complex matrices and let B be an hermitian matrix. Let Un(B) denote the unitary orbit of B in Mn(C) and let EA denote the trace preserving conditional expectation onto A. We give an spectral characterization of the set EA(Un(B)) = {EA(U B U) : U ∈ Mn(C), unitary matrix}. We obtain a similar result for the contractive orbit...
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...
متن کاملUnitary Matrices and Hermitian Matrices
Unitary Matrices and Hermitian Matrices Recall that the conjugate of a complex number a + bi is a − bi. The conjugate of a + bi is denoted a+ bi or (a+ bi)∗. In this section, I’ll use ( ) for complex conjugation of numbers of matrices. I want to use ( )∗ to denote an operation on matrices, the conjugate transpose. Thus, 3 + 4i = 3− 4i, 5− 6i = 5 + 6i, 7i = −7i, 10 = 10. Complex conjugation sati...
متن کاملWigner surmise for Hermitian and non-Hermitian chiral random matrices.
We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral random matrix theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in the microscopic large- N limit, we find an excellent agreement valid for a small number of exact zero eigenvalues. Compact expressions are derived for real eig...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(96)00029-8