COMPUTING THE NEAREST BISYMMETRIC POSITIVE SEMIDEFINITE MATRIX UNDER THE SPECTRAL RESTRICTION 双对称半正定矩阵特征值矩阵范数数值计算光谱限制Let A and C denote real n × n matrices. Given real n-vectors x1,……… ,xm,m≤n,and a set of numbers (L)={λ1,λ2…λm},We descrbe(Ⅰ)the set...
(positive semidefinite) matrix is A > 0 (⩾ 0). Unless otherwise mentioned, a real symmetric or a complex Hermitian positive definite matrix will be referred to as a positive definite matrix. A symmetric positive definite matrix A admits the Cholesky factorization A = HHT, where H is a lo...
Advances in Linear Algebra & Matrix TheoryMartin Slawski, Ping Li, and Matthias Hein. Regularization-free estimation in trace regression with symmetric positive semidefinite matrices. In NIPS, 2015.Slawski, M., Li, P. & Hein, M. (2015) Regularization-free estimation in trace regression with ...
A real symmetric matrix A = ||aij|| (i, j = 1, 2, …, n) is said to be positive (nonnegative) definite if the quadratic form Q(x) = Σni, j=1 aijxixj is positive (nonnegative) for all x = (x1…, xn)≠ (0, …, 0). It is known that A is a positive (nonnegative...
In the present paper, we argue that such regularization may no longer be necessary if the underlying matrix is symmetric positive semidefinite ( extsf{spd}) and the design satisfies certain conditions. In this situation, simple least squares estimation subject to an extsf{spd} constraint may ...
Random matrix theory improved Fr\\'echet mean of symmetric positive definite matrices In this study, we consider the realm of covariance matrices in machine learning, particularly focusing on computing Fr茅chet means on the manifold of symme... F Bouchard,A Mian,M Tiomoko,... 被引量: 0发表...
Problem for the week of February 1, 2010 Let A be an n × n real symmetric positive definite matrix. If B is an n × m real matrix, show that BT AB is positive semidefinite. Also show that rank(BT AB) = rankB, so that BT AB is positive definite if and only if B has rank ...
参见 AntisymmetricMatrixQ HermitianMatrixQ AntihermitianMatrixQ SymmetricMatrix PositiveSemidefiniteMatrixQ Transpose SymmetrizedArray Symmetrize相关指南 矩阵判断 矩阵和线性代数 历史 2008版本中引入 (7.0) | 2014版本中被更新 (10.0) 按以下格式引用: Wolfram Research (2008),SymmetricMatrixQ,Wolfram 语言函数,...
Higher-Order (Fαφ )β Vector-Pseudoquasi-Type IHigher-Order DualityMinimax Fractional Type ProgrammingPositive Semidefinite Symmetric MatrixConvexity and generalized convexity play important roles in optimization theory. With the development of programming problem, there has been a growing interest in ...
2) symmetric positive semidefinite solution 对称半正定解 1. The symmetric positive semidefinite solutions of the matrix equation (A TXA,B TXB)=(C,D) is considered in this paper. 讨论了矩阵方程(ATXA,BTXB)=(C,D)的对称半正定解。 更多例句>> 3) symmetrically positive semi definite matrix...