CompoundMatrix - Revision history

Benjamin Talbot: Capitalize variables in syntax and argument descriptions

2024-08-26T14:06:36Z

Capitalize variables in syntax and argument descriptions

Benjamin Talbot: Capitalized CompoundMatrix in example code

2024-08-26T14:02:17Z

Capitalized CompoundMatrix in example code

Benjamin Talbot: Reorder MATLAB output so it looks proper.

2024-08-24T02:09:44Z

Reorder MATLAB output so it looks proper.

Benjamin Talbot: Add restrictions to the arguments

2024-08-23T22:41:39Z

Add restrictions to the arguments

Benjamin Talbot: Changed/corrected update date and QETLAB version number.

2024-08-23T03:02:17Z

Changed/corrected update date and QETLAB version number.

Benjamin Talbot: Created page for CompoundMatrix (a couple edits ago, made some small changes)

2024-08-23T02:40:16Z

Created page for CompoundMatrix (a couple edits ago, made some small changes)

Benjamin Talbot at 02:34, 23 August 2024

2024-08-23T02:34:18Z

Benjamin Talbot: Created page with "{{Function |name=CompoundMatrix |desc=Computes the compound matrix of a given matrix |cat=Miscellaneous |upd=November 12, 2014 |v=0.50}}
2024-08-23T02:33:33Z

Created page with "{{Function |name=CompoundMatrix |desc=Computes the compound matrix of a given matrix |cat=Miscellaneous |upd=November 12, 2014 |v=0.50}} <t..."

New page
{{Function
|name=CompoundMatrix
|desc=Computes the compound matrix of a given matrix
|cat=[[List of functions#Miscellaneous|Miscellaneous]]
|upd=November 12, 2014
|v=0.50}}
<tt>'''CompoundMatrix'''</tt> is a [[List of functions|function]] that computes the ''r'' th [https://en.wikipedia.org/wiki/Compound_matrix compound matrix] of a given matrix.

==Syntax==
* <tt>comp = CompoundMatrix(A, r)</tt>

==Argument descriptions==
* <tt>A</tt>: A matrix.
* <tt>r</tt>: An integer denoting the size of the minors to compute.

==Example==
Taking the 2nd compound matrix involves calculating 2 by 2 minors of the matrix. For a 3 by 4 matrix, the entries for these minors can be indexed by the row index sets {1,2}, {1,3}, and {2,3} and the column index sets {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}. The computed values are placed in the resulting compound matrix according to the lexicographic ordering of the index sets. The following code shows an example:
<syntaxhighlight>
>> A = [1, 3, 7, 2; 8, 5, 3, 4; 6, 9, 0, 1]
>> r = 2
>> compoundMatrix(A, r)

A =

1 3 7 2
8 5 3 4
6 9 0 1

r =

2

ans =

-19 -53 -12 -26 2 22
-9 -42 -11 -63 -15 7
42 -18 -16 -27 -31 3
</syntaxhighlight>
Notice that the size of the resulting matrix is not necessarily the same size as the original matrix. In general, the size of the compound matrix is (''m'' choose ''r'' ) by (''n'' choose ''r'' ) for an ''m'' by ''n'' matrix.

{{SourceCode|name=Commutant}}

@@ Line 8: / Line 8: @@
 ==Syntax==
-* <tt>comp = CompoundMatrix(A, r)</tt>
+* <tt>COMP = CompoundMatrix(A, R)</tt>
 ==Argument descriptions==
 * <tt>A</tt>: An <tt>m</tt>-by-<tt>n</tt> matrix.
-* <tt>r</tt>: An integer denoting the size of the minors to compute. Must be between <tt>1</tt> and <tt>min{m, n}</tt>, inclusive. If <tt>r > min{m, n}</tt>, then the result is the <tt>0x0</tt> matrix.
+* <tt>R</tt>: An integer denoting the size of the minors to compute. Must be between <tt>1</tt> and <tt>min{m, n}</tt>, inclusive. If <tt>R > min{m, n}</tt>, then the result is the <tt>0x0</tt> matrix.
 ==Example==

← Older revision		Revision as of 14:02, 26 August 2024
Line 33:		Line 33:


−	>> ~~compoundMatrix~~(A, r)	+	>> CompoundMatrix(A, r)

	ans =		ans =

@@ Line 18: / Line 18: @@
 <syntaxhighlight>
 >> A = [1, 3, 7, 2; 8, 5, 3, 4; 6, 9, 0, 1]
 A =
@@ Line 29: / Line 26: @@
 r =
@@ Line 35: / Line 33: @@
 ans =

@@ Line 3: / Line 3: @@
 |desc=Computes the compound matrix of a given matrix
 |cat=[[List of functions#Miscellaneous|Miscellaneous]]
-|upd=August 22, 2024
+|upd=August 23, 2024
 |v=0.90}}
 <tt>'''CompoundMatrix'''</tt> is a [[List of functions|function]] that computes the ''r'' <sup>th</sup> [https://en.wikipedia.org/wiki/Compound_matrix compound matrix] of a given matrix.
@@ Line 11: / Line 11: @@
 ==Argument descriptions==
-* <tt>A</tt>: A matrix.
+* <tt>A</tt>: An <tt>m</tt>-by-<tt>n</tt> matrix.
-* <tt>r</tt>: An integer denoting the size of the minors to compute.
+* <tt>r</tt>: An integer denoting the size of the minors to compute. Must be between <tt>1</tt> and <tt>min{m, n}</tt>, inclusive. If <tt>r > min{m, n}</tt>, then the result is the <tt>0x0</tt> matrix.
 ==Example==
-Taking the 2<sup>nd</sup> compound matrix involves calculating 2 by 2 minors of the matrix. For a 3 by 4 matrix, the entries for these minors can be indexed by the row index sets {1,2}, {1,3}, and {2,3} and the column index sets {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}. The computed values are placed in the resulting compound matrix according to the lexicographic ordering of the index sets. The following code shows an example:
+Taking the 2<sup>nd</sup> compound matrix involves calculating 2-by-2 minors of the matrix. For a 3-by-4 matrix, the entries for these minors can be indexed by the row index sets {1,2}, {1,3}, and {2,3} and the column index sets {1,2}, {1,3}, {1,4}, {2,3}, {2,4}, and {3,4}. The computed values are placed in the resulting compound matrix according to the lexicographic ordering of the index sets. The following code shows an example:
 <syntaxhighlight>
 >> A = [1, 3, 7, 2; 8, 5, 3, 4; 6, 9, 0, 1]
@@ Line 42: / Line 42: @@
   -18  -16  -27  -31    3
 </syntaxhighlight>
-Notice that the size of the resulting matrix is not necessarily the same size as the original matrix. In general, the size of the compound matrix is (''m'' choose ''r'' ) by (''n'' choose ''r'' ) for an ''m'' by ''n'' matrix.
+Notice that the size of the resulting matrix is not necessarily the same size as the original matrix. In general, the size of the compound matrix is (''m'' choose ''r'' )-by-(''n'' choose ''r'' ) for an ''m''-by-''n'' matrix.
 {{SourceCode|name=CompoundMatrix}}

← Older revision		Revision as of 02:34, 23 August 2024
Line 44:		Line 44:
	Notice that the size of the resulting matrix is not necessarily the same size as the original matrix. In general, the size of the compound matrix is (''m'' choose ''r'' ) by (''n'' choose ''r'' ) for an ''m'' by ''n'' matrix.		Notice that the size of the resulting matrix is not necessarily the same size as the original matrix. In general, the size of the compound matrix is (''m'' choose ''r'' ) by (''n'' choose ''r'' ) for an ''m'' by ''n'' matrix.

−	{{SourceCode\|name=~~Commutant~~}}	+	{{SourceCode\|name=CompoundMatrix}}