## Most recent change of Matrices

Edit made on October 26, 2008 by GuestEditor at 21:02:43

Deleted text in red / Inserted text in green

WW
Matrices is the plural of "matrix", which is a sort of "rectangular grid of numbers", like this ...

EQN:\left[\begin{matrix}a_1&a_2&a_3\\b_1&b_2&b_3\end{matrix}\right]

This is a matrix with two rows and three columns.
This is a matrix with two rows and three columns - it is a 2x3 matrix.

Adding matrices is easy - it only works if they're the same size, and you do it entry by entry.

Multiplying is much less obvious, but arises naturally by thinking of a matrix as a linear transformation from EQN:R^n to EQN:R^m. Thinking of matrix multiplication in that way makes it clear why division of matrices in not generally defined, but the inverse of a matrix will sometimes (but not always) exist.

Specifically, think of a matrix as a mapping from EQN:R^n to EQN:R^m and consider the space in EQN:R^m of all points that can be hit. If the dimension of that space is /n,/ then the mapping can be undone. That means the mapping has an inverse, and so the matrix has an inverse.

More later ...
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