Analytical formulas for calculating the extremal ranks of the matrix-valued function A +BXC when the rank of X is fixed
نویسنده
چکیده
Analytical formulas are established for calculating the maximal and minimal ranks of the matrix-valued function A+BXC when the rank of X is fixed. Some consequences are also given.
منابع مشابه
Analytical formulas for calculating the extremal ranks and inertias of A + BXB∗ when X is a fixed-rank Hermitian matrix
The rank of a matrix and the inertia of a square matrix are two of the most generic concepts in matrix theory for describing the dimension of the row/column vector space and the sign distribution of the eigenvalues of the matrix. Matrix rank and inertia optimization problems are a class of discontinuous optimization problems, in which decision variables are matrices running over certain matrix ...
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