Journal Article10.1137/0131050
Hermitian and Nonnegative Definite Solutions of Linear Matrix Equations
C. G. Khatri,Sujit Kumar Mitra +1 more
291
TL;DR: In this paper, necessary and sufficient conditions for existence and expressions for general Hermitian and nonnegative definite solutions are obtained for the following three systems of linear equations: (I) $AX = C, (II) $XB = D.
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Abstract: Necessary and sufficient conditions for existence and expressions for general Hermitian and nonnegative definite solutions are obtained for the following three systems of linear equations: (I) $AX = C$, (II) $AX = C,XB = D$, (III) $AXB = C$.
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Adi Ben-Israel,T. N. E. Greville +1 more
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TL;DR: In this paper, the Moore of the Moore-Penrose Inverse is described as a generalized inverse of a linear operator between Hilbert spaces, and a spectral theory for rectangular matrices is proposed.
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A Generalized inverse for matrices
Roger Penrose
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TL;DR: A generalization of the inverse of a non-singular matrix is described in this paper as the unique solution of a certain set of equations, which is used here for solving linear matrix equations, and for finding an expression for the principal idempotent elements of a matrix.
On best approximate solutions of linear matrix equations
Roger Penrose
- 01 Jan 1956
TL;DR: In this paper, it was shown how to define a generalized inverse of a non-singular matrix, which has relevance to the statistical problem of finding the best approximate solution of inconsistent systems of equations by the method of least squares.
826
Estimation of Variance and Covariance Components in Linear Models
TL;DR: In this article, a linear model in the form, where is an unknown parameter and ξ is a hypothetical random variable with a given dispersion structure but containing unknown parameters called variance and covariance components.
374