Orthogonal Matrices
Definition
An orthonormal (or orthogonal) matrix is a matrix whose columns are an orthonormal family of vectors.
Some authors call these real orthogonal or unitary matrices.
Notation
Let $A \in \F ^{m \times n}$.
Something something
\[
AA^\top = I.
\]
Characterizations
A matrix is orthonormal if and only if its
transpose product with the matrix is the
identity.
A matrix is orthonormal if and only if its
transpose is orthonormal.