From Wikipedia:

In linear algebra, a complex square matrix $U$ is unitary if its conjugate transpose $U^*$ is also its inverse, that is, if $U^{*} U = U U^{*}=I,$, where $I$ is the identity matrix. In physics, especially in quantum mechanics, the Hermitian adjoint of a matrix is denoted by a dagger ($\dagger$) and the equation above becomes $U^{\dagger} U = U U^{\dagger }=I.$

Are the terms "Hermitian matrix" and "unitary matrix" one and the same? If not, how are they different?


1 Answer 1


A hermitian Matrix $H$ has $H = H^\dagger \neq I$, where for a unitary matrix $U$ you have $U^\dagger = U^{-1}\neq U$.

They are the complex analogous to "symmetrical" and "orthogonal"


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