# 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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33 views

### Good concise, big picture, linear algebra book?

I have looked at this answer and am not satisfied with the results. Reference book for linear algebra applied to statistics? I have briefly looked at two of the books suggested by the answer, the one ...
9 views

### Intuitive explanation of Minimum Covariance Determinant (MCD)

I am an undergrad working on Anomaly Detection on an 8 dimensional dataset, with PYOD, which relies on the MCD in the sklearn's MinCovDet. I tried reading Minimum Covariance Determinant and Extensions,...
28 views

### This is how I understand why the denominator of the root mean square is raised to the power of 1/2. Am I on the right track?

I've been going through some threads (see links below) and also a lot of introductory statistics textbooks to try to understand why in the formula for the root mean square, the denominator is also ...
3 views

### Algebra for Intervention Effect in Interrupted Time Series (with delayed effect)

I have run an interrupted time series analysis using GLS regression model in R. My data consists of 48 observations [time 1:48], with the intervention implemented at time 20, but it's effect not ...
18 views

### PCA dimension reduction on correlation matrix for invertability

I have a non-singular (correlation) matrix $C$ of dimension $N{\times}N$, this is a modified version of another correlation matrix, and therefore I don't think I am able to apply any calculations on ...
17 views

### Published source for D-dimensional behaviour of Dot-Product

I am currently studying the behaviour of the dot product between two random vectors in $R^d$. Specifically I wanted to start with the case of uniform random vectors on $\mathcal{S}^{d-1}$. I found ...
34 views

### Is the variance of an estimator equal to the variance of error and the SSE of a regression?

Is the variance of an estimator equal to the variance of error? $Var(β) = σ^2$ Since $Var(β)=E[εε']$ and $E[εε'] = Var(σ) = σ^2$ ? Additionally why is it that the expression for $Var(β) = E[εε']$ ...
39 views

### Rank of sample covariance matrix when $p = n$

Suppose we have a $p$-dimensional Gaussian distribution, and we take $n$ observations from that distribution. This answer states that when $p > n$, then the sample variance covariance matrix is ...
55 views

### Is $tr(B(B^TWB + D)^{-1}B^TW) = tr((I + D(B^TWB)^{-1})^{-1})$?

I am reading Eilers and Marx (1996) and at the beginning of page 94 they write, for $Q = B^TWB$, $D$ a symmetric positive definite matrix and $W$ a diagonal matrix, \begin{align} tr\left(B(Q + D)^{-1}...
14 views

### Connection between samples and dimensions of a matrix with the covariance matrix in PCA

In PCA, for a given matrix $M_{S\times D}$ where s = samples and d = dimensions, computing covariance matrix of dimension vector and then an eigen decomposition on it leads to eigenvectors which can ...
Assume I want to solve a regression problem $AX=B$ , the matrix A is a thin matrix and rank deficient i.e, the nullity of $A$ is non-empty , i want a solution for which the block entries of $x$ are in ...