A unitary transformation, often shortened to a unitary transform, is a bijective linear transformation 
on a Hermitian
inner product space that satisfies 
for all 
. It preserves the norm and
angles. In finite dimensions, its matrix 
in an orthonormal
basis is a unitary matrix, so 
. On a real inner
product space, the corresponding map is an orthogonal
transformation.
Conjugation by 
gives a similarity transformation of
a square matrix 
,
 |
where 
denotes the conjugate transpose.
