这个概念来自泛函分析,其中半正定矩阵(positive semidefinite matrices)定义正算子(positive operators)。 如果两个矩阵 A 和 B 满足 B-A \succeq 0 ,我们可以定义一个非严格偏序( non-strict partial order) B \succeq A,它是自反的、反对称的和传递的( reflexive, antisymmetric, and transitive;); ...
Positive semidefinite (PSD) and positive definite (PD) matrices are closely connected with Euclidean distance matrices. Accordingly, they play a central role in this monograph. This chapter reviews some of the basic results concerning these matrices. Among the topics discussed are various ...
Agler, J., Helton, J., McCullough, S., Rodman, L.: Positive Semidefinite Matrices with a Given Sparsity Pattern. Linear Algebra Appl. 107, 101–149 (1988)Agler, J., Helton, W., McCullough, S., Rodman, L.: Positive semidefinite matrices with a given sparsity pattern. Linear Algebra...
Let A and B be positive semidefinite matrices of the same size. Using a trace inequality of Ando, Hiai, and Okubo, we prove that ‖B1−tA2t−1B1−t+A1−tB2t−1A1−t‖2≤‖A+B‖2 for t∈[12,34], where ‖.‖2 denotes the Hilbert-Schmidt norm. This gives an affimat...
We show how to compute a relative-error low-rank approximation to anypositive semidefinite (PSD) matrix in sublinear time, i.e., for any $n imesn$ PSD matrix $A$, in $ilde O(n \\cdot poly(k/\\epsilon))$ time we output arank-$k$ matrix $B$, in factored form, for which $...
Perturbation analysis of the Hermitian positive definite solution of the matrix equation X AX2A = I 热度: 人工智能基础(第2版) x2d;高济 x2d;ai x2d;4 x2d;本 热度: Not Positive Definite Matrices--Causes and Cures 热度: Optimization(Repetition) ...
Using a quasilinear representation for unitarily invariant norms, we prove a basic inequality: Let A= L X X ∗ M be positive semidefinite, where X∈ M m,n. Then |||X| p|| 2⩽‖L p‖ ‖M p‖ for all p>0 and all unitarily invariant norms ‖·‖. We show how several inequ...
R. Hill, "On the cone of positive semidefinite matrices," Linear Algebra Appl., vol. 90, pp. 81-88, 1987.HILL R,WATERS S.On the cone of positive semidefinite matrices[J].Linear Algebra Appl,1987,90:81-88.HILL R,WATERS S.On the cone of positive semidefinite matrices. Linear Algebra ...
Learn about positive definiteness and semidefiniteness of real and complex matrices. Learn how definiteness is related to the eigenvalues of a matrix. With detailed examples, explanations, proofs and solved exercises.
The inverse problems of a class of positive semidefinite centro symmetric matrices were considered,the expression of the solution was provided.And the optimal approximation of this class of matrices was discussed,the existence and uniqueness of the solution of this problem is obtained.关键词: positive...