LMIs in Control/pages/Basic Matrix Theory

Basic Matrix NotationEdit

Consider the complex matrix  .

 


Transpose of a Matrix

The transpose of  , denoted as   or   is:

 


Adjoint of a Matrix

The adjoint or hermitian conjugate of  , denoted as   is:

 

Where   is the complex conjugate of matrix element  .

Notice that for a real matrix  ,  .

Important Properties of MatriciesEdit

Hermitian, Self-Adjoint, and Symmetric Matricies

A square matrix   is called Hermitian or self-adjoint if  .

If   is Hermitian then it is called symmetric.


Unitary Matricies

A square matrix   is called unitary if   or  .


External LinksEdit