Can the basis minor of a matrix be the matrix itself?

  • #1
mairzydoats
35
3
Hello

I am trying to learn linear algebra, and I came across this definition of basis minor on this webpage:

https://en.wikibooks.org/wiki/Linear_Algebra/Linear_Dependence_of_Columns

"The rank of a matrix is the maximum order of a minor that does not equal 0. The minor of a matrix with the order of the rank of the matrix is called a basis minor of the matrix, and the columns that the minor includes are called the basis columns."

Does this mean that if the determinant of the matrix does not equal zero, then its basis minor is just itself, and its rank is just the same as its order?

Thank you
 

Answers and Replies

  • #2
Geofleur
Science Advisor
Gold Member
426
177
That sounds right. For an ## n \times n ## matrix, the order of a minor is allowed to be the same as ## n ##. If the determinant of the whole matrix does not vanish, then rank is ## n ##, and the order of the largest non-vanishing minor is also ## n ##.
 
  • Like
Likes mairzydoats
  • #3
mairzydoats
35
3
For an ## n \times n ## matrix, the order of a minor is allowed to be the same as ## n ##.

Thanks Geofleur. I thought so but just wasn't sure.
 

Suggested for: Can the basis minor of a matrix be the matrix itself?

Replies
12
Views
2K
Replies
5
Views
208
  • Last Post
Replies
34
Views
1K
Replies
34
Views
905
  • Last Post
Replies
3
Views
699
Replies
1
Views
327
Replies
1
Views
87
Replies
7
Views
205
  • Last Post
Replies
9
Views
595
Top