Solution of certain matrix equations
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- by John Jones PDF
- Proc. Amer. Math. Soc. 31 (1972), 333-339 Request permission
Abstract:
The main purpose of this paper is to obtain solutions of matrix equations of the following types, $AX - XB = C,XDX + AX + XB + C = 0$, in which case $X$ is an unknown $n$ by $n$ matrix and $A,B,C,D$ are $n$ by $n$ matrices having elements belonging to the field $C$ of complex numbers. Results obtained extend those of W. E. Roth, J. E. Potter and others concerning the existence and the representation of solutions $X$ of the above equations.References
- R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406–413. MR 69793
- James E. Potter, Matrix quadratic solutions, SIAM J. Appl. Math. 14 (1966), 496–501. MR 201457, DOI 10.1137/0114044
- William E. Roth, The equations $AX-YB=C$ and $AX-XB=C$ in matrices, Proc. Amer. Math. Soc. 3 (1952), 392–396. MR 47598, DOI 10.1090/S0002-9939-1952-0047598-3 —, On the matrix equation ${X^2} + AX + XB + C = 0$, Proc. Amer. Math. Soc. 1 (1950), 586-589. MR 12, 471.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 31 (1972), 333-339
- MSC: Primary 15A24
- DOI: https://doi.org/10.1090/S0002-9939-1972-0292863-0
- MathSciNet review: 0292863