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2009•Journal of MathematicsRequires access

FURTHER ANALYSIS ON A DETERMINANT INEQUALITY

Yang Zhong-peng

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Abstract

In this ariticle, the main purpose is to improve the upper bound of the determinant of the sum of two complex matrices. By using the implements of the more precise determinant inequality of two Hermitian positive definite matrices, and by the result of the relationship among the determinants described by the quardratic inequality, we obtain a new upper bound of the sum of two complex matrices. As an application of our results, we improve the upper bound of Hua Loo Keng’s determinant inequality.

About this research paper

What this paper is about

In this ariticle, the main purpose is to improve the upper bound of the determinant of the sum of two complex matrices. By using the implements of the more precise determinant inequality of two Hermitian positive definite matrices, and by the result of the relationship among the determinants described by the quardratic inequality, we obtain a new upper bound of the sum of two complex matrices. As an application of our results, we improve the upper bound of Hua Loo Keng’s determinant inequality.

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Available abstract

In this ariticle, the main purpose is to improve the upper bound of the determinant of the sum of two complex matrices. By using the implements of the more precise determinant inequality of two Hermitian positive definite matrices, and by the result of the relationship among the determinants described by the quardratic inequality, we obtain a new upper bound of the sum of two complex matrices. As an application of our results, we improve the upper bound of Hua Loo Keng’s determinant inequality.

Key concepts: Mathematics, Upper and lower bounds, Inequality, Hermitian matrix, Positive-definite matrix, Combinatorics, Pure mathematics, Mathematical analysis

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