Linear algebra is concerned with vector spaces of all dimensions and linear transformations between them, including systems of linear equations, bases, dimensions, subspaces, matrices, determinants, traces, eigenvalues and eigenvectors, diagonalization, Jordan forms, etc. For questions specifically ...

learn more… | top users | synonyms

2
votes
1answer
170 views
+50

Curve scaled by vector.

Given a closed curve $C$ which is defined as a set of vectors pointing to each point $V_a$. Let the curve's "range" be $0 \leq a \leq 1$. Let the normal vector pointing outwardly tangent of ...
0
votes
0answers
28 views
+50

Bayesian statistics and Basis for continous functions

I was thinking about Bayesian statistics, and one thought bothered me: In Bayesian statistics, we assume that the pdf $p(x)$ can be described as: $p(x)=\int f(x|\theta)g(\theta)d\theta$ usually ...
13
votes
6answers
1k views
+50

What is the idea behind a projection operator? What does it do?

I know what a projection operator is, but I am unable to explain it in words without using mathematical symbols. Can anyone help me? I don't need examples or the definition - I want to know why and ...
-1
votes
1answer
153 views
+50

Finding the Dimension of a Matrix Polynomial: $W$ = { $p(B)$ : $p$ is a polynomial with real coefficients}

Let $W = \{ p(B) : p \text{ is a polynomial with real coefficients}\}$, where $$B= \begin{pmatrix} 0 & 1 & 0\\ 0 & 0 & 1\\ 1 & 0 & 0 \end{pmatrix}$$ The dimension $d$ of the ...
3
votes
2answers
113 views
+200

General Steinitz exchange lemma

Where can I find a proof of the following general Steinitz exchange lemma: Let $B$ be a basis of a vector space $V$, and $L\subset V$ be linearly independent. Then there is an injection ...