Cofactor matrix

[Ed Suh]

Hi,

I constructed a matrix using -matrix- command, and is there a way to find the cofactor matrix with a command?

Thank you!

[Andrew Musau]

I cannot find a Mata function that does this, but you can easily calculate this by multiplying each element of the inverse by the determinant and transposing the resulting matrix. The inverse and determinant can be obtained using the functions -luinv()- and -det()-, respectively.

mata
A = (1,2,3\0,4,5\1,0,6)
A
(det(A)*luinv(A))'
end

Res.:

: A = (1,2,3\0,4,5\1,0,6)

: A
       1   2   3
    +-------------+
  1 |  1   2   3  |
  2 |  0   4   5  |
  3 |  1   0   6  |
    +-------------+

: (det(A)*luinv(A))'
         1     2     3
    +-------------------+
  1 |   24     5    -4  |
  2 |  -12     3     2  |
  3 |   -2    -5     4  |
    +-------------------+

[Ed Suh]

Oh, I see!! Thank you very much.

Can we use -det- and -luinv- to find the cofactor matrix of for instance, A_12?

[Andrew Musau]

See

help matrix_extraction

Directly, without creating the matrix, you can do something like

mata
A = (1,2,3\0,4,5\1,0,6)
A
(det(A[1..2, 1..2])*luinv(A[1..2, 1..2]))'
end

Res.:

: A = (1,2,3\0,4,5\1,0,6)

:
: A
       1   2   3
    +-------------+
  1 |  1   2   3  |
  2 |  0   4   5  |
  3 |  1   0   6  |
    +-------------+

:
: (det(A[1..2, 1..2])*luinv(A[1..2, 1..2]))'
        1    2
    +-----------+
  1 |   4    0  |
  2 |  -2    1  |
    +-----------+

[Ed Suh]

Thank you very much!

I will try this method!