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Determinant of the Sum of a Symmetric and a Skew-Symmetric Matrix

SIAM Journal on Matrix Analysis and Applications, 1997
The set of all possible determinant values of the sum of a (complex) symmetric matrix and a skew-symmetric matrix with prescribed singular values is determined. This set can also be viewed as the best containment region for the determinant of a square matrix $X$ in terms of the singular values of its symmetric and skew-symmetric parts. The technique is
Natália Bebiano   +2 more
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Symmetric Matrix Means

Linear Algebra and its Applications, 2022
Mitsuru Uchyama
semanticscholar   +1 more source

An algorithm for matrix symmetrization

Journal of the Franklin Institute, 1981
Abstract In this paper we characterize a symmetrizability property using the theory of output sets. Employing the basic properties of symmetric matrices and an efficient algorithm for systematic generation of output sets, an algorithm for testing the symmetrizability of a matrix is presented and illustrated.
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An iterative algorithm for locating the minimal eigenvector of a symmetric matrix

IEEE International Conference on Acoustics, Speech, and Signal Processing, 1984
A new iterative method of finding the minimum eigenvalue of a symmetric matrix is described. This method does not utilize matrix inversions and is applicable to any matrix R for which the matrix-vector product Rx is rapidly computable.
D. Fuhrmann, Bede Liu
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Maximum a posterior linear regression with elliptically symmetric matrix variate priors

EUROSPEECH, 1999
In this paper, elliptic symmetric matrix variate distribution is proposed as the prior distribution for maximum a posterior linear regression (MAPLR) based model adaptation.
W. Chou
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A survey of conjugate gradient algorithms for solution of extreme eigen-problems of a symmetric matrix

IEEE Transactions on Acoustics Speech and Signal Processing, 1989
A survey of various conjugate gradient (CG) algorithms is presented for the minimum/maximum eigen-problems of a fixed symmetric matrix. The CG algorithms are compared to a commonly used conventional method found in IMSL.
Xiaopu Yang, T. Sarkar, E. Arvas
semanticscholar   +1 more source

Symmetric Matrix Derivatives with Applications

Journal of the American Statistical Association, 1982
Abstract Dwyer (1967) provided extensive formulas for matrix derivatives, many of which are for derivatives with respect to symmetric matrices. The results of his article are only for symmetric matrices whose (j, i) element is considered to differ from the (i, j) element even though their scalar values are equal.
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On the Sum of the Largest Eigenvalues of a Symmetric Matrix

SIAM Journal on Matrix Analysis and Applications, 1992
The sum of the largest k eigenvalues of a symmetric matrix has a well-known extremal property that was given by Fan in 1949 [Proc. Nat. Acad. Sci., 35 (1949), pp. 652–655].
M. Overton, R. Womersley
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Response Matrix of Symmetric Nodes

Nuclear Science and Engineering, 1984
Properties of a symmetric node's response matrix are discussed. The node may have an internal structure such that it remains invariant under the symmetry transformations of the considered node. A transformation diagonalizing the response matrix is given by means of symmetry considerations.
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On computing an equivalent symmetric matrix for a nonsymmetric matrix

International Journal of Computer Mathematics, 1988
A real or a complex symmetric matrix is defined here as an equivalent symmetric matrix for a real nonsymmetric matrix if both have the same eigenvalues. An equivalent symmetric matrix is useful in computing the eigenvalues of a real nonsymmetric matrix. A procedure to compute equivalent symmetric matrices and its mathematical foundation are presented.
Sen, SK, Venkaiah, VC
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