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Approximating a Symmetric Matrix [PDF]
Psychometrika, 1990 We examine the least squares approximation C to a symmetric matrix B, when all diagonal elements get weight w relative to all nondiagonal elements. When B has positivity p and C is constrained to be positive semi-definite, our main result states that, when w ≥1/2, then the rank of C is never greater than p, and when w ≤1/2 then the rank of C is at ...
R. A. Bailey, John C. Gower
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Householder's tridiagonalization of a symmetric matrix
Numerische Mathematik, 1968In an early paper in this series [4] Householder’s algorithm for the tridiagonalization of a real symmetric matrix was discussed. In the light of experience gained since its publication and in view of its importance it seems worthwhile to issue improved versions of the procedure given there.
C. Reinsch +2 more
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Decomposition of a symmetric matrix
Numerische Mathematik, 1976An algorithm is presented to compute a triangular factorization and the inertia of a symmetric matrix. The algorithm is stable even when the matrix is not positive definite and is as fast as Cholesky. Programs for solving associated systems of linear equations are included.
Linda Kaufman +2 more
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Mass matrix with symmetric mixing
Physical Review D, 1991Extending the work of Barnhill, we propose distributing the mixing matrix between the up and down quarks equally. With this choice of gauge eigenstates, the resulting mixing matrix in the new basis is simply the identity and the gauge bosons couple to these states in an essentially trivial manner.
T. S. Santhanam +2 more
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Symmetric Matrix Eigenvalue Techniques
2006The article describes symmetric matrix eigenvalue techniques: basic methods (power method, inverse iteration, orthogonal iteration and QR iteration), tridiagonalization and implicitly shifted QR method, divide-and-conquer method, bisection and inverse iteration, the method of multiple relatively robust representations, Jacobi method and Lanczos method.
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Determinant of the Sum of a Symmetric and a Skew-Symmetric Matrix
SIAM Journal on Matrix Analysis and Applications, 1997The 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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An algorithm for matrix symmetrization
Journal of the Franklin Institute, 1981Abstract 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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Symmetric Matrix Derivatives with Applications
Journal of the American Statistical Association, 1982Abstract 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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Response Matrix of Symmetric Nodes
Nuclear Science and Engineering, 1984Properties 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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