Xiong Hui-jun
Abstract
A criterion for the positive definiteness of symmetric 3 × 3 block-matrix A is presented.Applying the criterion,we derive the necessary and sufficient conditions for that the matrix equation(AT XA,B TXB) =(C,D) has positive definite solution.The expression of the general solution is given.
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A criterion for the positive definiteness of symmetric 3 × 3 block-matrix A is presented.Applying the criterion,we derive the necessary and sufficient conditions for that the matrix equation(AT XA,B TXB) =(C,D) has positive definite solution.The expression of the general solution is given.
Key concepts: Positive definiteness, Positive-definite matrix, Mathematics, Definiteness, Block (permutation group theory), Matrix (chemical analysis), Applied mathematics, Symmetric matrix