Hector Miranda | Universidad del Bio-bio (original) (raw)
Related Authors
Centro de Investigación Científica y de Educación Superior de Ensenada, BC.
Uploads
Papers by Hector Miranda
Proyecciones, Aug 1, 2003
There are well known inequalities for Hermitian matrices A and B that relate the diagonal entries... more There are well known inequalities for Hermitian matrices A and B that relate the diagonal entries of A+B to the eigenvalues of A and B. These inequalities are easily extended to more general inequalities in the case where the matrices A and B are perturbed through congruences of the form U AU * + V BV * , where U and V are arbitrary unitary matrices, or to sums of more than two matrices. The extremal cases where these inequalities and some generalizations become equalities are examined here.
Linear Algebra and its Applications, 2000
For complex matrices A and B there are inequalities related to the diagonal elements of AB and th... more For complex matrices A and B there are inequalities related to the diagonal elements of AB and the singular values of A and B. We study the conditions on the matrices for which those inequalities become equalities. In all cases, the conditions are both necessary and sufficient.
Linear Algebra and its Applications, 1994
A group induced preorder on matrix space permits the description of the convex hulls of sets of p... more A group induced preorder on matrix space permits the description of the convex hulls of sets of proper and improper real matrices with given singular values, and also permits a new proof of the necessity of the known relations between the diagonal elements and singular values of a real matrix.
Linear algebra and its applications, 1996
The von Neumann trace inequality for singular values is reexamined by determining the possible va... more The von Neumann trace inequality for singular values is reexamined by determining the possible values for the diagonal elements contributing to the trace. The possible values for the eigenvalues contributing to the trace are also found.
Linear algebra and its applications, 1993
For futed real or complex matrices A and B, the well-known von Neumann trace inequality identifie... more For futed real or complex matrices A and B, the well-known von Neumann trace inequality identifies the maximum of ItdUAVB)], as U and V range over the unitary group, the maximum being a bilinear expression in the singular values of A and B. This paper establishes the analogue of this inequality for real matrices A and B when U and V range over the proper (real) orthogonal group. The maximum is again a bilinear expression in the singular values, but there is a subtracted term when A and B have determinants of opposite sign. John von Neumann [l] proved a half century ago that if A and B are square matrices with complex elements, then sup Itr(UAVB)) = a,fil + a,&
Proyecciones, Aug 1, 2003
There are well known inequalities for Hermitian matrices A and B that relate the diagonal entries... more There are well known inequalities for Hermitian matrices A and B that relate the diagonal entries of A+B to the eigenvalues of A and B. These inequalities are easily extended to more general inequalities in the case where the matrices A and B are perturbed through congruences of the form U AU * + V BV * , where U and V are arbitrary unitary matrices, or to sums of more than two matrices. The extremal cases where these inequalities and some generalizations become equalities are examined here.
Linear Algebra and its Applications, 2000
For complex matrices A and B there are inequalities related to the diagonal elements of AB and th... more For complex matrices A and B there are inequalities related to the diagonal elements of AB and the singular values of A and B. We study the conditions on the matrices for which those inequalities become equalities. In all cases, the conditions are both necessary and sufficient.
Linear Algebra and its Applications, 1994
A group induced preorder on matrix space permits the description of the convex hulls of sets of p... more A group induced preorder on matrix space permits the description of the convex hulls of sets of proper and improper real matrices with given singular values, and also permits a new proof of the necessity of the known relations between the diagonal elements and singular values of a real matrix.
Linear algebra and its applications, 1996
The von Neumann trace inequality for singular values is reexamined by determining the possible va... more The von Neumann trace inequality for singular values is reexamined by determining the possible values for the diagonal elements contributing to the trace. The possible values for the eigenvalues contributing to the trace are also found.
Linear algebra and its applications, 1993
For futed real or complex matrices A and B, the well-known von Neumann trace inequality identifie... more For futed real or complex matrices A and B, the well-known von Neumann trace inequality identifies the maximum of ItdUAVB)], as U and V range over the unitary group, the maximum being a bilinear expression in the singular values of A and B. This paper establishes the analogue of this inequality for real matrices A and B when U and V range over the proper (real) orthogonal group. The maximum is again a bilinear expression in the singular values, but there is a subtracted term when A and B have determinants of opposite sign. John von Neumann [l] proved a half century ago that if A and B are square matrices with complex elements, then sup Itr(UAVB)) = a,fil + a,&