Jacobi formula

  • Thread starter TimeRip496
  • Start date
  • #1
254
5

Main Question or Discussion Point

Can anyone explain to me what is the cofactor matrix? I have trouble finding on the net the intuition behind it. Likewise what is the meaning of the adjugate matrix?
 

Answers and Replies

  • #2
Matterwave
Science Advisor
Gold Member
3,965
326
This is a lesson in linear algebra. Probably it would be good to consult your linear algebra book about this for a thorough understanding.

A cofactor matrix is a matrix whose entries are the cofactors of some other matrix. While the adjugate matrix is simply the transpose of the cofactor matrix.

Hopefully you learned how to take co-factors when finding determinants. The cofactor of some entry ##A_{ij}## in a matrix ##\bf{A}## is the determinant of the resulting matrix when you delete the ith row and j'th column of the matrix ##\bf{A}## and then accounting for an alternating sign, a factor of ##(-1)^{i+j}##.
 

Related Threads on Jacobi formula

  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
2
Views
3K
Replies
2
Views
1K
Replies
2
Views
3K
Top