一类矩阵特征值的不等式及其在Fischer不等式证明中的应用(An eigenvalue inequality of a class of matrices and its applications in proving the Fischer inequality)

Abstract

The Hadamard inequality and Fischer inequality play an important role in the matrix study. Many articles have addressed these inequalities providing new proofs, noteworthy extensions, generalizations, refinements, counterparts and applications. This paper discusses the eigenvalues of a class of matrices related to the real symmetric positive definite matrix and establishes an inequality of the eigenvalues. By using this inequality, the Fischer determinant inequality and Hadamard determinant inequality are proved.

Keywords

• positive definite matrix
• eigenvalue
• eigenvector
• determinant inequality