Displaying similar documents to “Inequalities involving Khatri-Rao products of positive semi-definite matrices.”

Matrix inequalities involving the Khatri-Rao product

Xian Zhang, Zhong Peng Yang, Chong-Guang Cao (2002)

Archivum Mathematicum

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We extend three inequalities involving the Hadamard product in three ways. First, the results are extended to any partitioned blocks Hermitian matrices. Second, the Hadamard product is replaced by the Khatri-Rao product. Third, the necessary and sufficient conditions under which equalities occur are presented. Thereby, we generalize two inequalities involving the Khatri–Rao product.

Complete solution of tropical vector inequalities using matrix sparsification

Nikolai Krivulin (2020)

Applications of Mathematics

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We examine the problem of finding all solutions of two-sided vector inequalities given in the tropical algebra setting, where the unknown vector multiplied by known matrices appears on both sides of the inequality. We offer a solution that uses sparse matrices to simplify the problem and to construct a family of solution sets, each defined by a sparse matrix obtained from one of the given matrices by setting some of its entries to zero. All solutions are then combined to present the...

Some Special Matrices of Real Elements and Their Properties

Xiquan Liang, Fuguo Ge, Xiaopeng Yue (2006)

Formalized Mathematics

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This article describes definitions of positive matrix, negative matrix, nonpositive matrix, nonnegative matrix, nonzero matrix, module matrix of real elements and their main properties, and we also give the basic inequalities in matrices of real elements.