Editing Matrices
You are currently not logged in.
To change this, fill in the following fields:
Username
Password
If you want a password, email topicsinmaths@solipsys.co.uk
Who can read this page?
The World
Members
Council
Admin
You have been granted an edit lock on this page
until Fri Apr 26 00:22:50 2024.
Press
to finish editing.
Who can edit this page?
World editing disabled
Members
Council
Admin
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 - 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 ---- Further reading: * http://www.google.com/search?q=matrices * http://mathworld.wolfram.com/Matrix.html