# Questions tagged [linear-algebra]

A field of mathematics concerned with the study of finite dimensional vector spaces, including matrices and their manipulation, which are important in statistics.

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### Understanding a particular rotation strategy

I am trying to replicate the rotation strategy (for factors) in a paper. I will try to make as clear as possible what I don't understand. Let the model be: $X = F\Lambda + \epsilon$, where $F$ is Tx3 ...
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### If 2 linear combinations of 2 predictor variables (x1, x2) produce 2 outcome variables (y1, y2), what is cov(x2, y2)?

Assume that cor(x1, x2) means the correlation (Pearson's r) between x1 and x2, and cov(x1, x2) means the covariance between x1 and x2. Given the below assumptions: N = 1000 Both mean(x1) and mean(x2)...
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### R: linear algebra representation of the prediction operator for a mixed effects model

(See edit at the bottom for the bounty) I am trying to learn how to simulate LMM data with matrix linear algebra. So far I've managed to simulate a simple model with a random intercept: ...
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### Proof that if covariance is zero then there is no linear relationship

I get that a zero covariance doesn´t imply independence, but everybody says that if there is dependence and the covariance is zero then it is a non linear dependence. People base their interpretation ...
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### Intuition about how the formula for “variance of axis of angle $\alpha$ with horizontal axis” works (multiple correspondents analysis)

From the text : Multiple Correspondents Analysis by Brigette LeRoux the following is given (page 32). For the purposes of this post I'm just considering there to be two dimensions that point clouds ...
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### prove for Eckart-young in Frobenius norm

On page 74, linear algebra and learning from data. P74 the prove for Eckart-young in the frobenius norm. I couldnot understand why G = 0 in the proof, anybody can help me? Thank you!
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### (SVMs) Do the specific higher dimensional mappings of attributes not matter when calculating a kernel?

From what I know, one of the strategies employed by an SVM is to increase dimensionality of your data until they are linearly separable. (I guess there's some mathematical proof that your data will ...