# Random Sampling # Make an NxN rank-1 matrix N = 100 sampleRate = 0.1 A = np.dot(np.random.randn(N,1),np.random.randn(1,N)) # Make mask with random sampling mask = np.less(np.random.rand(N,N),sampleRate) # Zero out matrix where mask is 0 A[np.logical_not(mask)] = ...
简单来说rank-1约束就是对作为决策变量的矩阵X，要使得rank(X)=1。这类约束是矩阵补全（matrix comple...
For two distinct rank-1 matrices A and B , a rank-1 matrix C is called a separating matrix of A and B if the rank of A + C is 2 but the rank of B + C is 1 or vice versa. In this case, rank-1 matrices A and B are said to be separable . We show that every pair of...
\left[ \begin{matrix} c+3d\\ 2c+d \\ 3c+2d \end{matrix} \right] \ \\ 虽然有3个数,但是这三个数能不能表示三维空间中所有的向量\left[ \begin{matrix} a_1\\ a_2 \\ a_3 \end{matrix} \right] \ 我们令 c+3d = a_1\\ ...
In this paper, we study the problem of low-rank matrix sensing where the goal is to reconstruct a matrix {\em exactly} using a small number of linear measurements. Existing methods for the problem either rely on measurement operators such as random element-wise sampling which ...
已知一个positive definite matrix(正定矩阵)M的eigenvalue decomposition(特征值分解)为: M=QΣQ∗=QΣQT 这里Q是M的eigenvector组成的unitary matrix(酉矩阵),Σ是由M的eigenvalue组成的diagonal matrix. 令 M^=M+uuT, 这里u是一个column vector(列向量),所以uuT是一个rank 1 matrix 那么有没有方法快速计...
5) rank of matrix 矩阵的秩 1. By means of the rank of matrix, line outspreading, it gives some conditions in which a matrix can decompose to two Kronecker products of matrix. 对矩阵Kronecker积分解进行研究,通过矩阵的秩,行展开等方法,给出了将一个矩阵分解为两个矩阵Kronecker积的若干条件。
Our proof is original and the results are surprising in light of the fact that even the weighted rank-one matrix factorization problem is NP-hard in general. Next, we derive sample complexity bounds in terms of spectral properties of the signless Laplacian of the sampling matrix. Our proposed...
A theorem of Marcus and Moyls on linear transformations on matrices preserving rank 1 and a classical result of Frobenius on determinant preservers are re-proved by elementary matrix methods. Minc,Henryk - 《Linear & Multilinear Algebra》 被引量: 29发表: 2010年 A notion of rank for unitary ...
A linear iterative method for projective reconstruction based on rank 1 matrix containing the images of all points in all views,which can deal with all the images in a unified manner,is presented in the paper. 提出了一种能够将所有图像平等看待基于秩1的射影重建方法,该方法并不是直接求解射影空间...