Several Schur complement inequalities on block Hadamard product

Abstract

The Schur complement theory is very important in many areas such as statistics, matrix analysis, numerical analysis, and control theory. It is a powerful tool to discuss many significant results. This paper deals with the inequalities involving block Hadamard product of positive definite matrices. By using the definition and the properties of block Hadamard product, we obtain useful inequalities on the Schur complement of the block Hadamard product of two positive definite matrices and their inverses. Finally, we give some numerical examples which confirm our theoritical analysis.

Keywords

• Block matrices,block Hadamard product,Schur complement

References

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