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?
Why use a matrix?
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1The 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. – 2011-04-10
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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.
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0This is so mathy... now is there a more intuitive answer for Why would I want to use a matrix? – 2014-01-27
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Matrices describe how transformations act on a space in a way that we can easily compute with. See this Wikipedia article.