LMIs in Control/Tools/Basic Matrix Theory

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Basic Matrix Notation[edit]

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 Matricies[edit]

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 .


WIP, additional references to be added

External Links[edit]