Previous |  Up |  Next


Re-nonnegative define matrix; matrix equation; generalized singular value decomposition
An $n\times n$ complex matrix $A$ is called Re-nonnegative definite (Re-nnd) if the real part of $x^{\ast } Ax$ is nonnegative for every complex $n$-vector $x$. In this paper criteria for a partitioned matrix to be Re-nnd are given. A necessary and sufficient condition for the existence of and an expression for the Re-nnd solutions of the matrix equation $AXB=C$ are presented.
[1] Wu L., Cain B.: The Re-nonnegative definite solutions to matrix inverse problem $AX=B$. Linear Algebra Appl. 236 (1996), 137-146. MR 1375611
[2] Khatri C.G., Mitra S.K.: Hermitian and nonnegative definite solutions of linear matrix equations. SIAM J. Appl. Math. 31.4 (1976), 579-585. MR 0417212 | Zbl 0359.65033
[3] Chu K.E.: Singular value and general singular value decompositions and the solution of linear matrix equation. Linear Algebra Appl. 88/89 (1987), 83-98. MR 0882442
[4] Porter A.D., Mousouris N.: Ranked solutions of $AXC=B$ and $AX=B$. Linear Algebra Appl. 24 (1979), 217-224. MR 0524838 | Zbl 0411.15009
[5] Dai H.: On the symmetric solution of linear matrix equations. Linear Algebra Appl. 131 (1990), 1-7. MR 1057060
[6] Wang Q.W.: The metapositive definite self-conjugate solutions of the matrix equation $AXB=C$ over a skew field. Chinese Quarterly J. Math. 3 (1995), 42-51.
[7] Wang Q.W.: The matrix equation $AXB=C$ over an arbitrary skew field. Chinese Quarterly J. Math. 4 (1996), 1-5.
[8] Wang Q.W.: Skewpositive semidefinite solutions to the quaternion matrix equation $AXB=C$. Far East. J. Math. Sci., to appear. MR 1432967
[9] Paige C.C., Saunders M.A.: Towards a generalized singular value decomposition. SIAM J. Numer. Anal. 18 (1981), 398-405. MR 0615522 | Zbl 0471.65018
[10] Stewart G.W.: Computing the CS-decomposition of a partitioned orthogonal matrix. Numer. Math. 40 (1982), 297-306. MR 0695598
Partner of
EuDML logo