Difference between revisions of "CompoundMatrix"
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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= | + | |upd=August 23, 2024 |
| − | |v=0. | + | |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. | <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. | ||
==Syntax== | ==Syntax== | ||
| − | * <tt> | + | * <tt>COMP = CompoundMatrix(A, R)</tt> |
==Argument descriptions== | ==Argument descriptions== | ||
| − | * <tt>A</tt>: | + | * <tt>A</tt>: An <tt>m</tt>-by-<tt>n</tt> matrix. |
| − | * <tt> | + | * <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] | ||
| − | |||
| − | |||
| − | |||
A = | A = | ||
| Line 29: | Line 26: | ||
| + | >> r = 2 | ||
r = | r = | ||
| Line 35: | Line 33: | ||
| + | >> CompoundMatrix(A, r) | ||
ans = | ans = | ||
| Line 42: | Line 41: | ||
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}} | ||
Latest revision as of 14:06, 26 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]
A =
1 3 7 2
8 5 3 4
6 9 0 1
>> r = 2
r =
2
>> CompoundMatrix(A, r)
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.