Complex Matrices

Matrices with complex numbers

Conjugate

Definition

Let .
The conjugate of is

That is, the conjugate is applied to every entry of the matrix

Conjugate Transpose

Definition

Let .
The conjugate transpose is

Hermitian

Definition

Let .

is a Hermitian if

(See matrices equal theorem)

Remark

All Hermitian matrices are symmetric

Properties

  1. Distributive