# Transpose of conjugate transpose?

What is the transpose of a conjugate transpose? Let's say we have a matrix $$A$$ and its conjugate transpose $$A^{*}$$, would the transpose of the conjugate transpose be the conjugate of $$A$$, i.e. $$\bar{A}$$?

Would one represent that as follows:

$$A^{*T} = \bar{A}$$

I have seen this written out as numpy code, but I don't know how to represent it.

So you're right, the transpose of the conjugate transpose of a matrix $$A$$ is just the conjugate $$\bar A$$, although I think this notation is not heavily used in linear algebra.
• Which notation do you mean? The $A^{*T} = \bar{A}$, then how would one represent that? – Morgoth Jul 9 '19 at 9:36
• Its fine. For me, $\bar A$ is not heavily used in linear algebra. – Wuestenfux Jul 9 '19 at 9:40