在矩阵论中，正交矩阵（orthogonal matrix）是一个方块矩阵Q，其元素为实数，而且行与列皆为正交的单位矢量，使得该矩阵的转置矩阵为其逆矩阵：

其中，为单位矩阵。正交矩阵的行列式值必定为+1或-1，因为：

底下是一些重要的性质：

In linear algebra, an orthogonal matrix is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors), i.e.

where I is the identity matrix.

This leads to the equivalent characterization: a matrix Q is orthogonal if its transpose is equal to its inverse: