Square matrix

Matrix with the same number of rows and columns / From Wikipedia, the free encyclopedia

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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.

A square matrix of order 4. The entries form the main diagonal of a square matrix. For instance, the main diagonal of the 4×4 matrix above contains the elements a11 = 9, a22 = 11, a33 = 4, a44 = 10.

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 .