# Tagged Questions

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### Can singular value decomposition be applied to a matrix of $n\times 1$ size?

Can singular value decomposition be applied to a matrix of $n \times 1$ size (a vector)? Usually I see that matrix is of size of $n \times m$. Any example?
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### Choleski decomposition of the covariance matrix

I have a process described as $r_t = \mu + \Sigma_t^{1/2}z_t$ where $z_t$ is let's say a standard normal distribution residual and $\Sigma_t$ is the conditional covariance matrix. The $t$ stands ...
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### How to obtain the inverse of a matrix while solving an equation?

Given a matrix $A$, let us assume there is a equation: $Ax = b$ To solve for $x$, we can write: $x = A^{-1} b$ One way to obtain the inverse of A is by single value decomposition: Decomposition ...
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### Shrinkage of Schafer and Strimmer

As we all know that the sample covariance matrix $(S = (s_{ij}))$ is postive definite when the number of observations is smaller than the number of samples, that is n>p. But, the sample covariance ...
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### Interpretation of matrix factorization results

Matrix factorization methods are known to give good results pertaining to problems like movie recommendation. The method reduces the feature space, which is then used for recommendations. For example ...
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### How to find unknown correlation coefficients in a correlation matrix from known correlation coefficients? [duplicate]

I have a correlation matrix A given below. Here A should be a positive-definite matrix so that we can perform Cholesky decomposition of A. ...
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### Non-negative matrix factorization in recommender systems

As i understand, in NMF we should have our three matrices elements non-negative. But i can't understand how to do it so far. Shouldn't we just initialize our factor matrices at the start with random ...
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### Singular value and eigen-decomposition of a square symmetric matrix should be identical, but differ in sign

As far as I know, singular value decomposition (SVD) and eigendecomposition give the same result for symmetric square matrices. But when I check the results in R, that's not what I see. Please see ...
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### Maximally reducing the rank of a matrix by removing some rows or columns

I have a $N \times M$ matrix, and the rank of matrix, $r$, is near $\min(M,N)$. I want to minimize the rank by removing some of the rows or columns to get $r \ll \min(M,N)$. The goal is to achieve ...