Nonnegative definite and positive definite solutions to the matrix equation \(AXA^*=B\). (English) Zbl 0552.15009
The author finds necessary and sufficient conditions for a non-negative (positive) definite solution to the equation in the title to exist. Assuming that the conditions are satisfied he derives formulas for the general solutions that are advantageous over formulas known before. Now, it is enough to have a fixed generalized inverse of A or B to write down the general solution.
Reviewer: B.Reichstein
MSC:
| 15A24 | Matrix equations and identities |
| 15A09 | Theory of matrix inversion and generalized inverses |
| 15B48 | Positive matrices and their generalizations; cones of matrices |
References:
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