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Matrix identities involving multiplication and transposition

Karl Auinger, Igor Dolinka, Michael V. Volkov (2012)

Journal of the European Mathematical Society

We study matrix identities involving multiplication and unary operations such as transposition or Moore–Penrose inversion. We prove that in many cases such identities admit no finite basis.

Matrix inequalities involving the Khatri-Rao product

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

Archivum Mathematicum

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.

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