Unitary matrices

A unitary matrix is a complex matrix $U$ satisfying the condition

$U^{\dagger }U=UU^{\dagger }=I_{n}\,$

where $I$ is the identity matrix and Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle U^{\dagger }} is the conjugate transpose (also called the Hermitian adjoint) of $U$. Note this condition says that a matrix $U$ is unitary if and only if it has an inverse which is equal to its conjugate transpose Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle U^{\dagger }\,}

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle U^{-1}=U^{\dagger }.}

A unitary matrix in which all entries are real is called an orthogonal matrix.

References

• Unitary matrix entry in Wikipedia