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Definition D5306
Complex matrix conjugate transpose

Let $A \in \mathbb{C}^{N \times M}$ be a D999: Complex matrix such that
 (i) $$A = \begin{bmatrix} A_{1, 1} & A_{1, 2} & \cdots & A_{1, M} \\ A_{2, 1} & A_{2, 2} & \vdots & A_{2, M} \\ \vdots & \cdots & \ddots & \vdots \\ A_{N, 1} & A_{N, 2} & \cdots & A_{N, M} \end{bmatrix}$$
The conjugate transpose of $A$ is the D999: Complex matrix $$A^* : = \begin{bmatrix} \overline{A}_{1, 1} & \overline{A}_{2, 1} & \cdots & \overline{A}_{N, 1} \\ \overline{A}_{1, 2} & \overline{A}_{2, 2} & \vdots & \overline{A}_{N, 2} \\ \vdots & \cdots & \ddots & \vdots \\ \overline{A}_{1, M} & \overline{A}_{2, M} & \cdots & \overline{A}_{N, M} \end{bmatrix}$$

Let $A \in \mathbb{C}^{N \times M}$ be a D999: Complex matrix.
The conjugate transpose of $A$ is the D999: Complex matrix $$A^* : = \overline{A^T}$$
Children
 ▶ D6205: Conjugate symmetric complex matrix ▶ D6223: Normal complex matrix ▶ D2086: Orthonormal complex matrix