Nonnegative-definite and positive-definite solutions to the matrix equation \(\mathbb{A}\times\mathbb{A}^*=\mathbb{B}\) -- revisited
The author establishes a general Hermitian nonnegative-definite solution to the matrix equation \(A\times A^*=B\) \((A^*\) is the conjugate transpose of a complex matrix \(A)\) in a form which can be viewed as a corrected version of that derived by \textit{C. G. Khatri} and \textit{S. K. Mitra} [SIAM J. Appl. Math. 31, 579-585 (1976; Zbl 0359.65033)], and alternative version to that derived by \textit{J. K. Baksalary} [Linear Multilinear Algebra 16, 133-139 (1984; Zbl 0552.15009)]. By using the new representation he obtains solutions of minimal and maximal rank, respectively.
scientific article; zbMATH DE number 1563483