CompoundMatrix

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 2^nd 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    3

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.

Source code

Click here to view this function's source code on github.