Subjects Linear Algebra

Conjugate Transpose

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Conjugate Transpose


1. The problem is to understand the expression $A*$. 2. In mathematics, the symbol $*$ often denotes an operation such as multiplication or a special operator depending on context. 3. If $A$ is a variable or matrix, $A*$ could mean the conjugate transpose (Hermitian transpose) of $A$ in linear algebra. 4. The conjugate transpose $A^*$ of a matrix $A$ is obtained by taking the transpose and then taking the complex conjugate of each element. 5. For example, if $A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}$, then $$A^* = \begin{bmatrix} \overline{a} & \overline{c} \\ \overline{b} & \overline{d} \end{bmatrix}$$ where $\overline{a}$ denotes the complex conjugate of $a$. 6. If $A$ is a real matrix, then $A^*$ is simply the transpose $A^T$. 7. Without additional context, $A*$ is best interpreted as the conjugate transpose of $A$ in algebra or linear algebra. 8. If you have a specific $A$ or operation in mind, please provide more details for a precise answer.