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low-rank matrices with noise and high
low-rank matrices with noise and high

Extremal properties of ray-nonsingular matrices
Extremal properties of ray-nonsingular matrices

MATRICES part 2 3. Linear equations
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... where AI J is a matrix of dimension pI × qJ . We call such a matrix a block matrix. The partitioning can be carried out in many ways and is often suggested by the structure of the underlying problem. For square matrices the most important case is when M = N , and pI = qI , I = 1 : N . Then the diago ...
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... This operation is one of the most common in statistics, and the X'X matrix is a particularly useful one. Note what happens in the matrix multiplication process: the score of subject 1 on variable 1 (element X11 in X') is multiplied times itself (X11 in X), the product is then added to the square of ...
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... Matrix operations Multiplication of matrices by real numbers: If A = aij is an m  n matrix and   R, then the product of the number  and matrix A is the matrix C = cij of the same type m  n with elements cij = aij for i = 1, 2, …, m and j = 1, 2, …, n. We say: matrix C is -multiple of ma ...
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... In this theorem, ( ⋅ )∗ stands for complex conjugate transpose. For a matrix X, the notation X(1, :) denotes the first row of X, and X(:, 1) the first column. Hence, the state dimension of the realization (which determines the computational complexity of multiplications and inversions using state re ...
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Matrix completion



In mathematics, matrix completion is the process of adding entries to a matrix which has some unknown or missing values.In general, given no assumptions about the nature of the entries, matrix completion is theoretically impossible, because the missing entries could be anything. However, given a few assumptions about the nature of the matrix, various algorithms allow it to be reconstructed. Some of the most common assumptions made are that the matrix is low-rank, the observed entries are observed uniformly at random and the singular vectors are separated from the canonical vectors. A well known method for reconstructing low-rank matrices based on convex optimization of the nuclear norm was introduced by Emmanuel Candès and Benjamin Recht.
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