Why use a matrix?

Question

Why would I want to use a matrix? It's good for organizing a few numbers but I can't find too much use for them. Could someone explain?

The abstract idea about linear transformations is all well and good, but here are a few practical areas for application: Computer graphics (rotations, representing 3-dimensions in two dimensions, skewing images, etc) , probability, computer vision. I had reason to use a $560\times 560$ matrix in a personal project studying the game of contract bridge. — Thomas Andrews, Apr 10 '11 at 22:21

score 3 · Accepted Answer · answered Apr 10 '11 at 21:57

3

We use matrices to study linear transformations between vector spaces. In particular, suppose we have a linear transformation $T: V \to W$ between two vector spaces $V$ and $W$. Suppose we have an ordered basis of $V$ and an ordered basis of $W$. Then we can represent vectors in $V$ and $W$ as column vectors. We can then represent $T$ by a matrix.

answered Apr 10 '11 at 21:57

NebulousReveal

13,935

This is so mathy... now is there a more intuitive answer for Why would I want to use a matrix? – Pacerier Jan 27 '14 at 06:36

score 1 · Answer 2 · answered Apr 10 '11 at 21:58

1

Matrices describe how transformations act on a space in a way that we can easily compute with. See this Wikipedia article.

answered Apr 10 '11 at 21:58

Zev Chonoles

129,973

Why use a matrix?

2 Answers2