What are the properties of unitary transform

A unitary transform is a type of linear transformation that preserves the inner product of vectors. The properties of a unitary transform are important in various areas of mathematics and signal processing. Here are some key properties of a unitary transform:

1. Preservation of Inner Product:

   • The fundamental property of a unitary transform is that it preserves the inner product of vectors. Mathematically, if $?$ is a unitary transform and $?$ and $?$ are vectors, then $⟨??,??⟩=⟨?,?⟩$, where $⟨\cdot ,\cdot ⟩$