Orthogonal Matrix

linear-algebra

Definition

Orthogonal Matrix

An orthogonal matrix is a square matrix $Q$ such that

$$Q^{T}Q=I=Q{Q}^T.$$

Equivalently, the columns and rows of $Q$ form an orthonormal basis of ${\mathbb{R}}^n$.

An orthogonal matrix represents a linear map that preserves the Euclidean norm and angles.