# 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.

203 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
47 views

### Multi-class LDA (pairwise classification)

From this post: $w=S_{W}^{-1}(μ1−μ2),$ is used to estimate $w_{0}=\frac{1}{2}(μ_{1}−μ_{2})^{T}S_{W}^{-1}(μ_{1}−μ_{2})−log(\frac{P1}{P2}),$ However, this is for a situation where there are only 2 ...
29 views

61 views

### Laplace transform of sum of $N$ IID random variables where $N$ is itself random

Let $\{Y_i\}$ be a sequence of IID random variables so that $Y_i \sim Exp(\lambda)$ or equivalently $Y_i \sim CPH_1(1, -\lambda)$ (continuous phase-type distribution). Let $N$ be a discrete random ...
31 views

### What are some beginner's references on algebraically structured models, and what's their connection with group actions and Fourier transform?

Since I didn't get an answer, I asked it on mathoverflow. I'm looking at a short-term position, whose project is on estimation in algebraically structured models. It also mentions in the required ...
58 views

### Why does the smallest eigenvalue of the covariance matrix of a GMM equal the common variance?

I've been reading a paper "Introduction to Tensor Decompositions and Their Applications in Machine Learning". In it, the author describes an algorithm for estimating the means of the ...
16 views

### Show that ABA=0 if and only if B is of the form C-PCP for some symmetric matrix C

If B is a symmetric matrix such that ABA is well-defined, then show that ABA=0 if and only if B is of the form C-PACPA for some symmetric matrix C. PA here is the projection matrix of A.
86 views

### Probabilities concerning n-spheres

Let $S_{n-1}(R)=\{ {\bf x}\in {\mathbb{R}}^n : ||{\bf x}||^2=R^2\}$ be the sphere in ${\mathbb{R}}^n$ with radious $R>0.$ Let the projection map $\tau_m({\bf x})=(x_1,...,x_m)$ with $m\leq n.$ Now, ...
16 views

### Visualizing data using vectors

Say there are 10 houses and we have three pieces of information for each of them, area, nbedrooms, price I can view this as 10 different vectors in space where there are 3 axes. Basically 10 arrows ...
44 views

### Determine if orthogonal projection and full rank

Let $X=(X_1,X_2)$ be a $n \times p$ matrix of rank $p$, where $X_1$ is $n\times p_1$ and $X_2$ is $n\times p_2$. Let $P_1$ be orthogonal projection onto $C(X_1)$ and $P_2$ be orthogonal projection ...
34 views

### Using matrices to find estimates in GLMs

How do we use matrices to find estimates in Linear Models? A 4 × 400 relay race is run as follows. There are four runners, each of whom runs 400 meters. The first runner carries a baton, which she ...
27 views

### how to normalize data such that an estimated OLS regression vector has pre-specified length (= L_2 norm)

I have the following data: $n$ observations on $d$ variables $X$ and one outcome variable $Y$; i.e. $X$ is a $n \times d$ matrix and $Y$ an $n \times 1$ vector. I consider the following Ordinary Least ...
30 views

### How vector projection works behind SVD?

I was reading a blog on mathematical intuition behind SVD. Here, author pointed out three information we get after vector decomposition. The directions of projection — the unit vectors (v₁ and v₂) ...
24 views

### Condition numbers, invertibility and multicollinearity

The following is an excerpt from Greene's Regression Analysis (Seventh Edition): a) What does it mean to be "difficult" to invert a matrix accurately? Shouldn't all matrixes be either ...
77 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 ...
16 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 ...
81 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 ...
23 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 ...
29 views

80 views