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Some properties and inequalities on the generalized Khatri-Rao product of matrices. (Chinese. English summary) Zbl 1212.15046
Summary: Based on the definition of Kronecker product, Hadamard product and Khatri-Rao product, the generalized Khatri-Rao product of matrices \(A\) and \(B\), written as \(f(A, B)\), are defined. Some common properties on the generalized Khatri-Rao product and some special properties on generalized Khatri-Rao product of specific matrices, such as positive matrices, semi-positive matrices, nonnegative matrices and Hermite matrices, are presented. The operation of conjugate transpose on the generalized Khatri-Rao product is deduced out. Moreover, some important inequalities about the generalized Khatri-Rao product of the inverse matrices and square matrices are proved. At last, properties of the eigenvalue of the generalized Khatri-Rao product of semi-matrices are presented.
MSC:
15A45 Miscellaneous inequalities involving matrices
15A69 Multilinear algebra, tensor calculus
15B48 Positive matrices and their generalizations; cones of matrices
15A09 Theory of matrix inversion and generalized inverses
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