CompoundMatrix: Difference between revisions
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|desc=Computes the compound matrix of a given matrix | |desc=Computes the compound matrix of a given matrix | ||
|cat=[[List of functions#Miscellaneous|Miscellaneous]] | |cat=[[List of functions#Miscellaneous|Miscellaneous]] | ||
|upd=August | |upd=August 23, 2024 | ||
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<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. | <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. | ||
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==Argument descriptions== | ==Argument descriptions== | ||
* <tt>A</tt>: | * <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== | ==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> | <syntaxhighlight> | ||
>> A = [1, 3, 7, 2; 8, 5, 3, 4; 6, 9, 0, 1] | >> A = [1, 3, 7, 2; 8, 5, 3, 4; 6, 9, 0, 1] | ||
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42 -18 -16 -27 -31 3 | 42 -18 -16 -27 -31 3 | ||
</syntaxhighlight> | </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}} | {{SourceCode|name=CompoundMatrix}} | ||
Revision as of 22:41, 23 August 2024
| CompoundMatrix | |
| Computes the compound matrix of a given matrix | |
| Other toolboxes required | none |
|---|---|
| Function category | Miscellaneous |
CompoundMatrix is a function that computes the r th compound matrix of a given matrix.
Syntax
- comp = CompoundMatrix(A, r)
Argument descriptions
- A: An m-by-n matrix.
- r: An integer denoting the size of the minors to compute. Must be between 1 and min{m, n}, inclusive. If r > min{m, n}, then the result is the 0x0 matrix.
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:
>> 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 3Notice 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.
Source code
Click here to view this function's source code on github.