Du, Juan; Feng, Sichen; Fan, Xiaotao Some properties and inequalities on the generalized Khatri-Rao product of matrices. (Chinese. English summary) Zbl 1212.15046 J. Nat. Sci. Hunan Norm. Univ. 32, No. 3, 7-9, 22 (2009). 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 Keywords:Khatri-Rao product; Hadamard product; Kronecker product; positive matrix; semi-positive matrix; nonnegative matrix; Hermite matrix; inequalities; inverse matrices; eigenvalue; semi-matrices PDF BibTeX XML Cite \textit{J. Du} et al., J. Nat. Sci. Hunan Norm. Univ. 32, No. 3, 7--9, 22 (2009; Zbl 1212.15046)