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This paper mainly discusses some properties of matrices under the similarity of unitary matrix. At the same time, we characterize the product of the eigenvalues of semi-positive definite matrices. Then we prove the rationality of the function operation of the Hermite matrix. Finally, we discuss the relationship between the singular values of the matrix and its sub matrix.doi:10.20431/2347-3142.0701003 fatcat:hq4xlny6f5fnfmpqaftxredpry