L-structured matrices and linear matrix equations∗
- 1 September 1983
- journal article
- research article
- Published by Taylor & Francis in Linear and Multilinear Algebra
- Vol. 14 (1), 67-88
- https://doi.org/10.1080/03081088308817543
Abstract
Conditions for the existence of solutions, and the general solution of linear matrix equations are given, when it is known a priori that the solution matrix has a given structure (e.g. symmetric, triangular, diagonal). This theory is subsequently extended to matrix equations that are linear in several unknown ‘structured’ matrices, and to partitioned matrix equations.Keywords
This publication has 16 references indexed in Scilit:
- The Elimination Matrix: Some Lemmas and ApplicationsSIAM Journal on Algebraic Discrete Methods, 1980
- The matrix equation AXB+CYD=ELinear Algebra and its Applications, 1980
- The matrix equation AX − YB = CLinear Algebra and its Applications, 1979
- The Commutation Matrix: Some Properties and ApplicationsThe Annals of Statistics, 1979
- Vec and vech operators for matrices, with some uses in jacobians and multivariate statisticsThe Canadian Journal of Statistics / La Revue Canadienne de Statistique, 1979
- On the matrix equations $AX - XB = C$ and $AX - YB = C$SIAM Journal on Applied Mathematics, 1977
- Explicit Solutions of Linear Matrix EquationsSIAM Review, 1970
- Some Theorems on Matrix Differentiation with Special Reference to Kronecker Matrix ProductsJournal of the American Statistical Association, 1969
- Some matrix equations over a finite fieldAnnali di Matematica Pura ed Applicata (1923 -), 1957
- A generalized inverse for matricesMathematical Proceedings of the Cambridge Philosophical Society, 1955