Wang Boying & Zhang Fuzhen , Some inequalities for the eigenvalues of the product of positive semidefinite Hermitian Matrices , L inearAlgebra A ppl. , 160(1992) , 113 - 118B. Wang and F. Zhang, "Some inequalities for the eigenvalues of the product of positive semidefinite Hermitian ...
We show that a matrix is a Hermitian positive semidefinite matrix whose nonzero entries have modulus 1 if and only if it is similar to a direct sum of all I's matrices and a 0 matrix via a unitary monomial similarity. In particular, the only such nonsingular matrix is the identity ...
More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector , where denotes the conjugate transpose of . Positive semi-definite matrices are defined s...
Let A be an Hermitian matrix If A is positive definite (resp., positive semidefinite), then all of its principal submatrices are positive definite (resp., positive semidefinite) Proof Let α be a proper subset of {1,…,n} and consider the principal submatrix A[α] ...
positive semidefinite form 半正定型,正半定形式 negative semidefinite matrix 负半定矩阵,半负定矩阵 positive matrix 正矩阵 positive definite matrix 正定矩阵 essentially positive matrix 本性正矩阵 positive real matrix 正实阵 positive definite Hermitian matrix 正定埃尔米特矩阵 相似...
2.4.8 Positive Definite Matrix A real symmetric matrix A is positive definite (positive semidefinite) if xT Ax > 0 (⩾ 0) for every nonzero vector x. Similarly, a complex Hermitian matrix A is positive definite (positive semidefinite) if x* Ax > 0 (⩾ 0) for every nonzero complex...
测试3×3 Hermitian 矩阵是否为半正定矩阵: In[1]:= Out[1]= 范围(10) 选项(1) 应用(13) 属性和关系(13) 可能存在的问题(2) 参见 PositiveDefiniteMatrixQNegativeDefiniteMatrixQNegativeSemidefiniteMatrixQHermitianMatrixQSymmetricMatrixQEigenvaluesSquareMatrixQ...
1)Hermitian positive definite matrixHermitian正定矩阵 1.Furthermore, a new estimation of the lower bound of the determinant module on the Hadamard product of a Hermitian positive definite matrix and a quasi-generalized complex positive definite matrix is obtained by using the improvement and the prope...
12.Estimates for Elgenvalues of Product of Positive Semidefinite Hermitian Matrices半正定Hermite矩阵之积的特征值估计 13.The Positive Semi-definite of Gram Matrix and it's Application格拉姆(Gram)矩阵的半正定性及其应用 14.On Partial Ordering of Pseudo-Schur Complement for Positive Semidefinite Block Matr...
Hermitian正定矩阵 1. Furthermore, a new estimation of the lower bound of the determinant module on the Hadamard product of a Hermitian positive definite matrix and a quasi-generalized complex positive definite matrix is obtained by using the improvement and the properties of quasi-generalized complex...