GenGellMann - Revision history

Nathaniel: Clarified identity matrix

2025-04-08T15:50:18Z

Clarified identity matrix

← Older revision		Revision as of 15:50, 8 April 2025
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	\|upd=December 18, 2013		\|upd=December 18, 2013
	\|v=0.50}}		\|v=0.50}}
	<tt>'''GenGellMann'''</tt> is a [[List of functions\|function]] that produces generalized Gell-Mann matrices. That is, it produces Hermitian matrices that form a traceless orthogonal basis for the space of $d \times d$ complex matrices.		<tt>'''GenGellMann'''</tt> is a [[List of functions\|function]] that produces generalized Gell-Mann matrices. That is, it produces Hermitian matrices that form a traceless orthogonal basis for the space of $d \times d$ complex matrices, together with the identity matrix.

	==Syntax==		==Syntax==
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	==Argument descriptions==		==Argument descriptions==
	* <tt>IND1</tt> and <tt>IND2</tt>: Integers between <tt>0</tt> and <tt>DIM-1</tt>, inclusive. If <tt>IND1 == IND2</tt> then <tt>G</tt> will be diagonal. If <tt>IND1 < IND2</tt> then <tt>G</tt> will be real and have exactly 2 nonzero entries. If <tt>IND1 > IND2</tt> then <tt>G</tt> will be imaginary and have exactly 2 nonzero entries.		* <tt>IND1</tt> and <tt>IND2</tt>: Integers between <tt>0</tt> and <tt>DIM-1</tt>, inclusive. If <tt>IND1 == IND2</tt> then <tt>G</tt> will be diagonal (if both indices equal 0 then <tt>G</tt> will be the identity matrix, otherwise <tt>G</tt> will be traceless). If <tt>IND1 < IND2</tt> then <tt>G</tt> will be real and have exactly 2 nonzero entries. If <tt>IND1 > IND2</tt> then <tt>G</tt> will be imaginary and have exactly 2 nonzero entries.
	* <tt>DIM</tt>: The size of the output matrix.		* <tt>DIM</tt>: The size of the output matrix.
	* <tt>SP</tt> (optional, default 0): A flag (either 1 or 0) indicating that the generalized Gell-Mann matrix produced should or should not be sparse.		* <tt>SP</tt> (optional, default 0): A flag (either 1 or 0) indicating that the generalized Gell-Mann matrix produced should or should not be sparse.

Nathaniel at 15:15, 29 September 2014

2014-09-29T15:15:21Z

← Older revision		Revision as of 15:15, 29 September 2014
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	\|name=GenGellMann		\|name=GenGellMann
	\|desc=Produces a generalized Gell-Mann operator		\|desc=Produces a generalized Gell-Mann operator
	~~\|req=[[opt_args]]~~
	\|rel=[[GellMann]]<br />[[GenPauli]]<br />[[Pauli]]		\|rel=[[GellMann]]<br />[[GenPauli]]<br />[[Pauli]]
			\|cat=[[List of functions#Special_states,_vectors,_and_operators\|Special states, vectors, and operators]]
	\|upd=December 18, 2013		\|upd=December 18, 2013
	\|v=1.00}}		\|v=0.50}}
	<tt>'''GenGellMann'''</tt> is a [[List of functions\|function]] that produces generalized Gell-Mann matrices. That is, it produces Hermitian matrices that form a traceless orthogonal basis for the space of $d \times d$ complex matrices.		<tt>'''GenGellMann'''</tt> is a [[List of functions\|function]] that produces generalized Gell-Mann matrices. That is, it produces Hermitian matrices that form a traceless orthogonal basis for the space of $d \times d$ complex matrices.

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	==Examples==		==Examples==
	===Gives the Pauli operators when <tt>DIM = 2</tt>===		===Gives the Pauli operators when <tt>DIM = 2</tt>===
	<~~pre~~>		<syntaxhighlight>
	>> GenGellMann(0,0,2) % identity		>> GenGellMann(0,0,2) % identity

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	1 0		1 0
	0 -1		0 -1
	</~~pre~~>		</syntaxhighlight>

	===Gives the Gell-Mann operators when <tt>DIM = 3</tt>===		===Gives the Gell-Mann operators when <tt>DIM = 3</tt>===
	<~~pre~~>		<syntaxhighlight>
	>> GenGellMann(0,1,3)		>> GenGellMann(0,1,3)

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	0 0.5774 0		0 0.5774 0
	0 0 -1.1547		0 0 -1.1547
	</~~pre~~>		</syntaxhighlight>

	===In Higher Dimensions===		===In Higher Dimensions===
	Generalized Gell-Mann matrices can be generated in arbitrary dimensions. It is recommended that you set <tt>SP = 1</tt> if <tt>DIM</tt> is large in order to save memory.		Generalized Gell-Mann matrices can be generated in arbitrary dimensions. It is recommended that you set <tt>SP = 1</tt> if <tt>DIM</tt> is large in order to save memory.
	<~~pre~~>		<syntaxhighlight>
	>> GenGellMann(2,3,4)		>> GenGellMann(2,3,4)

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	(206,35) 0.0000 + 1.0000i		(206,35) 0.0000 + 1.0000i
	(35,206) 0.0000 - 1.0000i		(35,206) 0.0000 - 1.0000i
	</~~pre~~>		</syntaxhighlight>

			{{SourceCode\|name=GenGellMann}}

	==External links==		==External links==
	* [http://en.wikipedia.org/wiki/Generalizations_of_the_Pauli_matrices Generalizations of the Pauli matrices] at Wikipedia		* [http://en.wikipedia.org/wiki/Generalizations_of_the_Pauli_matrices Generalizations of the Pauli matrices] at Wikipedia

Nathaniel: Created page with "{{Function |name=GenGellMann |desc=Produces a generalized Gell-Mann operator |req=opt_args |rel=GellMann
GenPauli
Pauli |upd=December 18, 2013 |v=1.0..."

2013-12-18T20:27:48Z

Created page with "{{Function |name=GenGellMann |desc=Produces a generalized Gell-Mann operator |req=opt_args |rel=GellMann<br />GenPauli<br />Pauli |upd=December 18, 2013 |v=1.0..."

New page

{{Function
|name=GenGellMann
|desc=Produces a generalized Gell-Mann operator
|req=[[opt_args]]
|rel=[[GellMann]]<br />[[GenPauli]]<br />[[Pauli]]
|upd=December 18, 2013
|v=1.00}}
<tt>'''GenGellMann'''</tt> is a [[List of functions|function]] that produces generalized Gell-Mann matrices. That is, it produces Hermitian matrices that form a traceless orthogonal basis for the space of $d \times d$ complex matrices.

==Syntax==
* <tt>G = GenGellMann(IND1,IND2,DIM)</tt>
* <tt>G = GenGellMann(IND1,IND2,DIM,SP)</tt>

==Argument descriptions==
* <tt>IND1</tt> and <tt>IND2</tt>: Integers between <tt>0</tt> and <tt>DIM-1</tt>, inclusive. If <tt>IND1 == IND2</tt> then <tt>G</tt> will be diagonal. If <tt>IND1 < IND2</tt> then <tt>G</tt> will be real and have exactly 2 nonzero entries. If <tt>IND1 > IND2</tt> then <tt>G</tt> will be imaginary and have exactly 2 nonzero entries.
* <tt>DIM</tt>: The size of the output matrix.
* <tt>SP</tt> (optional, default 0): A flag (either 1 or 0) indicating that the generalized Gell-Mann matrix produced should or should not be sparse.

==Examples==
===Gives the Pauli operators when <tt>DIM = 2</tt>===
<pre>
>> GenGellMann(0,0,2) % identity

ans =

1 0
0 1

>> GenGellMann(0,1,2) % Pauli X

ans =

0 1
1 0

>> GenGellMann(1,0,2) % Pauli Y

ans =

0.0000 + 0.0000i 0.0000 - 1.0000i
0.0000 + 1.0000i 0.0000 + 0.0000i

>> GenGellMann(1,1,2) % Pauli Z

ans =

1 0
0 -1
</pre>

===Gives the Gell-Mann operators when <tt>DIM = 3</tt>===
<pre>
>> GenGellMann(0,1,3)

ans =

0 1 0
1 0 0
0 0 0

>> GenGellMann(0,2,3)

ans =

0 0 1
0 0 0
1 0 0

>> GenGellMann(2,2,3)

ans =

0.5774 0 0
0 0.5774 0
0 0 -1.1547
</pre>

===In Higher Dimensions===
Generalized Gell-Mann matrices can be generated in arbitrary dimensions. It is recommended that you set <tt>SP = 1</tt> if <tt>DIM</tt> is large in order to save memory.
<pre>
>> GenGellMann(2,3,4)

ans =

0 0 0 0
0 0 0 0
0 0 0 1
0 0 1 0

>> GenGellMann(205,34,500,1) % a 500-by-500 sparse generalized Gell-Mann matrix

ans =

(206,35) 0.0000 + 1.0000i
(35,206) 0.0000 - 1.0000i
</pre>

==External links==
* [http://en.wikipedia.org/wiki/Generalizations_of_the_Pauli_matrices Generalizations of the Pauli matrices] at Wikipedia

GenGellMann - Revision history

Nathaniel: Clarified identity matrix

Nathaniel at 15:15, 29 September 2014

Nathaniel: Created page with "{{Function |name=GenGellMann |desc=Produces a generalized Gell-Mann operator |req=opt_args |rel=GellMannGenPauliPauli |upd=December 18, 2013 |v=1.0..."

Nathaniel: Created page with "{{Function |name=GenGellMann |desc=Produces a generalized Gell-Mann operator |req=opt_args |rel=GellMann
GenPauli
Pauli |upd=December 18, 2013 |v=1.0..."