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Results tagged with matrix
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A matrix (plural matrices) is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. The individual items in a matrix are called its elements or entries.
11
votes
Frobenius norm of a product of Gaussian matrices
Let $X$ be $d\times d$ a random matrix with iid $\mathcal N(0, 1/d)$ elements. …
- 107k
3
votes
Ways to modify data minimally while the variables to follow the desired covariances
\:\:\mathbf Z^\top\mathbf Z = \mathbf I,$$ which is solved in Find a matrix with orthonormal columns with minimum Frobenius distance to the given matrix. …
- 107k
99
votes
Why the sudden fascination with tensors?
A usual $n\times p$ data matrix is an example of a 2D tensor according to this definition.
This is not how tensors are defined in mathematics and physics! … One example of a real tensor in statistics would be a covariance matrix. …
7
votes
Is every correlation matrix positive definite?
The answers by @yoki and @MarkLStone (+1 to both) both point out that a population correlation matrix can have zero eigenvalues if variables are linearly related (such as e.g. … See Why is a sample covariance matrix singular when sample size is less than number of variables? and Why is the rank of covariance matrix at most $n-1$? …
- 107k
769
votes
Accepted
Relationship between SVD and PCA. How to use SVD to perform PCA?
It is a symmetric matrix and so it can be diagonalized: $$\mathbf C = \mathbf V \mathbf L \mathbf V^\top,$$ where $\mathbf V$ is a matrix of eigenvectors (each column is an eigenvector) and $\mathbf L$ … is a diagonal matrix with eigenvalues $\lambda_i$ in the decreasing order on the diagonal. …
- 107k