Square matrix
Matrix with the same number of rows and columns / From Wikipedia, the free encyclopedia
In mathematics, a square matrix is a matrix with the same number of rows and columns. An n-by-n matrix is known as a square matrix of order . Any two square matrices of the same order can be added and multiplied.
![Thumb image](http://upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Arbitrary_square_matrix.gif/320px-Arbitrary_square_matrix.gif)
Square matrices are often used to represent simple linear transformations, such as shearing or rotation. For example, if is a square matrix representing a rotation (rotation matrix) and
is a column vector describing the position of a point in space, the product
yields another column vector describing the position of that point after that rotation. If
is a row vector, the same transformation can be obtained using
, where
is the transpose of
.