ConjugateTranspose

Complex conjugate of a number or conjugate transpose of a matrix.

Syntax

If z is a number, then ConjugateTranspose(z) is the complex conjugate of z.
If A is a matrix, then ConjugateTranspose(A) is the conjugate transpose of A.

Vectors are treated like column matrices. Hence,

If v is a vector, then ConjugateTranspose(v) is the row matrix containing the complex conjugate entries of v.

The * postfix operator is implemented by the ConjugateTranspose function.

(1 + 3⋅i)*

1 − 3⋅i

❨5, 0, i❩*

( 5   0  −i)

A ≔ ❨❨2, 1, −i❩, ❨1, 0, 2❩, ❨4, i, 2❩, ❨0, 1, −1❩❩

⎛ 2   1  −i⎞
⎜ 1   0   2⎟
⎜ 4   i   2⎟
⎝ 0   1  −1⎠

A*

⎛ 2   1   4   0⎞
⎜ 1   0  −i   1⎟
⎝ i   2   2  −1⎠