ThmDex – An index of mathematical definitions, results, and conjectures.
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Complex matrix conjugate transpose
Definition D2086
Orthonormal complex matrix
Formulation 3
Let $\mathbb{C}^{N \times 1}$ be a D6080: Standard inner product space of complex column matrices.
Let $A \in \mathbb{C}^{N \times N}$ be a D999: Complex matrix such that
(i) \begin{equation} A = \begin{bmatrix} A_1 & A_2 & \cdots & A_N \end{bmatrix} \end{equation}
Then $A$ is an orthonormal complex matrix if and only if $A_1, \ldots, A_N$ is an D10: Orthonormal collection in $\mathbb{C}^{N \times 1}$.
Children
D5982: Orthonormal real matrix