Orthogonal Real Matrices
Definition
An orthogonal matrix is a matrix $U \in \R ^{n \times n}$ whose columns are orthonormal. Since an orthogonal matrix has $n$ columns, its columns are a basis for $\R ^n$.
An orthogonal matrix is a matrix $U \in \R ^{n \times n}$ whose columns are orthonormal. Since an orthogonal matrix has $n$ columns, its columns are a basis for $\R ^n$.