The Rank of a Matrix, the Value of a Determinant, and the Solution of a System of Linear EquationsFirst page of articledoi:10.1002/sapm1932111146RiceLepine HallJournal of Mathematics & Physics
Definition: the rank of a matrix Rank in linear algebra is a number that we assign to any matrix. It is the maximal number of linearly independent rows of the matrix. Equivalently, though it's not at all obvious at first glance, it is also the maximal number of linearly independent colum...
The affine rank minimization problem consists of finding a matrix of minimum rank that satisfies a given system of linear equality constraints. Such problems have appeared in the literature of a diverse set of fields including system identification and control, Euclidean embedding, and collaborative fil...
Integral operators with positive-semidefinite (PSD) kernels play a central role in the theory of reproducing kernel Hilbert spaces (RKHSs) and their applications; see for instance [4,5,19,20,26]. As an important instance, this class of operators encompasses the PSD matrices. Under suitable con...
We elaborate on the deviation of the Jordan structures of two linear relations that are finite-dimensional perturbations of each other. We compare their nu
Q Shi,H Lu,YM Cheung - 《IEEE Transactions on Neural Networks & Learning Systems》 被引量: 9发表: 2017年 Rank-one Solutions for Homogeneous Linear Matrix Equations over the Positive Semidefinite Cone The problem of finding a rank-one solution to a system of linear matrix equations arises from...
Complex systems are high-dimensional nonlinear dynamical systems with heterogeneous interactions among their constituents. To make interpretable predictions about their large-scale behaviour, it is typically assumed that these dynamics can be reduced to a few equations involving a low-rank matrix describing...
We establish the formulas of the maximal rank of a 3x3 partial banded block matrix where X and Y are a pair variant quaternion matrices subject to linear quaternion matrix equations A_1X = C_1,XB_1=C_2,A_3X B_3=C_3,A_2Y = D_1,Y B_2=D_2. As an application,we compare the...
例如,假设有以下两个矩阵A和B: A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} \\ 它们的哈达玛积C为: C = A \circ B = \begin{bmatrix} 1 \times 5 & 2 \times 6 \\ 3 \times 7 & 4 \times 8 \end...
This paper studies the problem of deterministic rank-one matrix completion. It is known that the simplest semidefinite programming relaxation, involving mi