# 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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### Vec operator and covariance matrix

You have a matrix containing $T$ observations of each of $K$ random variables \begin{align} U = \begin{bmatrix} u_{11} & \dots & u_{1T} \\ \vdots & \ddots & \vdots ...
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### Pseudo-inverse matrix for multivariate linear regression

In Andrew Ng's Machine Learning course lecture 4.6 on "Normal Equation", he says that in order to minimize $J(\theta) = \frac{1}{2m}\sum\limits_{i=1}^{m}({h_{\theta}}(x^{(i)}) - y^{(i)})^2$, ...
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### How to find a non-linear manifold for an implicit linear function in the neighborhood of a seed point?

I am trying to understand functional analysis as an infinite-dimensional extension of linear-analysis. In this process, I came across the above query and willing to get a solution and validation of ...
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### Solving for Z when Z^T Z = A using R

First time question asker here! Thanks in advance for any suggestions! So here's the issue. I start with a matrix Z which is samples by features. I create a covariance matrix $A = Z^T Z$. Then I ...
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### how to adjust a result for a variable

Okay. I'm not sure if I'm phrasing it well but here is the problem. I have a set of data which comes out as a density measurement of proteins, these are expressed in a numerical values and correspond ...
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### Derivation of skewness and kurtosis algebra of random variables

In algebra of random variables, the symbolic rule for computing variance of random variable $X\in\mathbb{R}^{n\times p}$ multiplied by a coefficent vector, $a\in\mathbb{R}^p$, is \text{Var}(X\cdot a)...
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### What's the importance of parallel eigenvectors?

I'm studying eigenvectors. I read that if a matrix is symmetric and if the eigenvalues are real numbers, the eigenvectors will be perpendicular. However, I have no idea what it means (if anything) ...