GellMann

GellMann
Produces a Gell-Mann operator
Other toolboxes required	none
Related functions	GenGellMann GenPauli Pauli
Function category	Special states, vectors, and operators

GellMann is a function that produces the 3-by-3 Gell-Mann matrices, as defined here:

\(g_0 = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\)	\(g_1 = \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\)	\(g_2 = \begin{bmatrix} 0 & -i & 0 \\ i & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix}\)	\(g_3 = \begin{bmatrix} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 0 \end{bmatrix}\)	\(g_4 = \begin{bmatrix} 0 & 0 & 1 \\ 0 & 0 & 0 \\ 1 & 0 & 0 \end{bmatrix}\)
	\(g_5 = \begin{bmatrix} 0 & 0 & -i \\ 0 & 0 & 0 \\ i & 0 & 0 \end{bmatrix}\)	\(g_6 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{bmatrix}\)	\(g_7 = \begin{bmatrix} 0 & 0 & 0 \\ 0 & 0 & -i \\ 0 & i & 0 \end{bmatrix}\)	\(g_8 = \frac{1}{\sqrt{3}} \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & -2 \end{bmatrix}\)

Syntax

• G = GellMann(IND)
• G = GellMann(IND,SP)

Argument descriptions

• IND: An index indicating which Gell-Mann operator you would like to be generated. Should be an integer between 0 and 8, inclusive.
• SP (optional, default 0): A flag (either 1 or 0) indicating that the Gell-Mann operator produced should or should not be sparse.

Examples

>> GellMann(1)

ans =

     0     1     0
     1     0     0
     0     0     0

>> GellMann(3,1) % the matrix produced here will be sparse

ans =

   (1,1)        1
   (2,2)       -1

Source code

Click on "expand" to the right to view the MATLAB source code for this function.

External links

• Gell-Mann matrices at Wikipedia