Hermitian matrixPositive semi-definite matrixEigenvaluesHadamard productsThe Schur theorem provides the global bounds for spectrum of the Hadamard product of two positive semi-definite matrices. In this paper, we obtain lower and upper estimations for each eigenvalue of th...
Eigenvalues estimation of Hadamard product of two Hermitian matrices%两个Hermitian矩阵的Hadamard乘积的特征值估计 来自 万方 喜欢 0 阅读量: 39 作者:杨忠鹏,冯晓霞 摘要: Schur定理规定了半正定矩阵的Hadamard乘积的所有特征值的整体界限.Eric Iksoon Im在同样的条件下确定了每个特征值的特殊的界限.本文给出了...
2.2.5 Special Matrices 2 1 Consider a square matrix A of order n. Then, if: (35)A=A*A˜ A† A is said to be real, symmetric, Hermitian (or self-adjoint), respectively. 2 If: (36)A−1=A˜ A† A is said to be orthogonal or unitary, respectively....
The inequalities obtained extend the result of Liu et al. 1. Introduction Let Mn be the set of n×n complex matrices. If X is positive semidefinite, we put X≥0. For two Hermitian matrices X,Y∈Mn,X≥Y means X−Y is positive semidefinite. If X is positive definite, we put X>...
[1] For complex matrices, Hermitian means conjugate symmetric, which in the real case reduces to simply symmetric. The theorem of Pólya and Szegö is actually valid for Hermitian matrices, but I simplified the statement for the case of real-valued matrices....
Nature of problem: The symmetrization of products of Hermitian operators is a well-known problem. Such a symmetrization process would be very time consuming when considering an operator made of the product of more than two terms. According to two different scenarios, the calculation of fully symmet...
3. 实对称矩阵都能被分解为 A=Q\Lambda Q^T 的形式,如果是normal Hermitian matrix则可以被分解为 A=UDU^* 的形式。 其中U为unitary matrix即共轭矩阵和逆矩阵相同的矩阵( UU^*=U^*U=I_n,~U^*=U^{-1},~|\lambda_n|=1,~|det(U)|=1) Lemma 3.2 Let B be a psd of size n and rank r...
the quantity obtained by multiplying the corresponding coordinates of each of two vectors and adding the products, equal to the product of the magnitudes of the vectors and the cosine of the angle between them. Also calleddot product,scalar product. ...
· qT T ∈Hermr (F )+ x∈L\V r ⊗F A∞F T (x)=T A p-adic arithmetic inner product formula 225 as a formal power series indexed by totally semi-positive definite hermitian matrices T over E/F of rank r, with terms that are special cycles Z(x)L ∈ CHr (XL) indexed by ...
Large gap asymptotics at the hard edge for product random matrices and Muttalib-Borodin ensembles We study the distribution of the smallest eigenvalue for certain classes of positive-definite Hermitian random matrices, in the limit where the size of the... C Tom,G Manuela,S Dries - 《Internatio...