matrix with rank 2. Is 0 an eigenvalue of A? (c) Let A be a matrix with Then ( ) A. A is the identity matrix. B. 0 is an eigenvalue of A. C. the only possible eigenvalues of A are 1 and -1. D. the determinant of A is 1. ...
In the paper, we propose to express the factorization model in terms of the sum of rank-1 matrices. Then the sparse factors can be easily estimated by applying the concept of the Hierarchical Alternating Least Squares (HALS) algorithm which is still regarded as one of the most effective ...
Rank 1 Case. Consider a Hermitian matrix model under an external potential with spiked external source. When the external source is of rank 1, we compute the limiting d... Baik,Jinho,Wang,... - 《Imrn International Mathematics Research Notices》 被引量: 34发表: 2011年 Inequalities on the ...
Mutual information for symmetric rank-one matrix estimation: A proof of the replica formula Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed ...
It is worthy to notice that every semigroup of all rank r, r > l,nn matrices over a finite field has no finite basis of identities. Let G be an arbitrary variety of groups with a finite basis of identities. A finite basis of identities is constructed for the variety generated by all...
1. This paper summarizes the applications of elementary transformation of matrix in solving therank of a matrixor a set of vectors,calculating inverse matrix or system of linear equations,and solving the system of linear equations and the greatest common divisor of polynomials with examples,furthermo...
Numerical Linear Algebra with ApplicationsGuanghui Cheng, Zhida Song, Jianfeng Yang, and Jia Si. The bounds of the eigenvalues for rank-one modification of hermitian matrix. Numerical Linear Algebra with Applications, 21(1):98-107, 2014.
On the largest eigenvalue of a Hermitian random matrix model with spiked external source II. Higher rank cases This is the second part of a study of the limiting distributions of the top eigenvalues of a Hermitian matrix model with spiked external source under a gen... B Jinho,D Wang - ...
Version 1.0.1These functions were originally designed for tutorial purposes in teaching & learning matrix algebra ideas using R. In some cases, functions are provided for concepts or computations available elsewhere in R, but where the name is not obvious, e.g., R() for the rank of a matri...
We study a non-convex low-rank promoting penalty function, the transformed Schatten-1 (TS1), and its applications in matrix completion. The TS1 penalty, as... S Zhang,P Yin,J Xin - 《Communications in Mathematical Sciences》 被引量: 4发表: 2015年 Rank-1 Matrix Approximation-Based Channel...