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2007•Journal of Putian UniversityRequires access

Notes on Lower Bounds for Determinant of the Hadamard Product of Some Matrix Class

Yang Zhong-peng

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Abstract

It is pointed out that the lower bound for determinant of two H-matrices obtained by LI Yao-tang and ZHONG Cong-lei (Some estimations for eterminant of the Hadamard product of H-matrices,Journal of Computational Mathematics,2005,23(4)) is equivalent to that obtained by CHEN Shen-can (Some determinantal inequlities for Hadamard product of matrices,Linear Algebra Appl,2003,368). Using the invariance for determinant of the Hadamard product under the permutation similitude,larger corresponding lower bounds are presented.

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It is pointed out that the lower bound for determinant of two H-matrices obtained by LI Yao-tang and ZHONG Cong-lei (Some estimations for eterminant of the Hadamard product of H-matrices,Journal of Computational Mathematics,2005,23(4)) is equivalent to that obtained by CHEN Shen-can (Some determinantal inequlities for Hadamard product of matrices,Linear Algebra Appl,2003,368). Using the invariance for determinant of the Hadamard product under the permutation similitude,larger corresponding lower bounds are presented.

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Available abstract

It is pointed out that the lower bound for determinant of two H-matrices obtained by LI Yao-tang and ZHONG Cong-lei (Some estimations for eterminant of the Hadamard product of H-matrices,Journal of Computational Mathematics,2005,23(4)) is equivalent to that obtained by CHEN Shen-can (Some determinantal inequlities for Hadamard product of matrices,Linear Algebra Appl,2003,368). Using the invariance for determinant of the Hadamard product under the permutation similitude,larger corresponding lower bounds are presented.

Key concepts: Hadamard product, Hadamard's maximal determinant problem, Complex Hadamard matrix, Hadamard matrix, Hadamard's inequality, Mathematics, Hadamard transform, Product (mathematics)

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