Most recent change of Matrices
Edit made on October 26, 2008 by GuestEditor at 21:02:43
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Matrices is the plural of "matrix", which is a sort of "rectangular grid of numbers", like this ...
This is a matrix with two rows and three
columns. 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 ...
See also Matrix Transformation