How do I find out the principal minors of a $4\times 4$ matrix?

Question

How many principal minors can a $4\times 4$ matrix have?

Is there any general method using which I can found out the principal minors of any $n\times n$ matrix?

score 3 · Accepted Answer · answered Mar 21 '18 at 11:22

3

We have

answered Mar 21 '18 at 11:22

user

Thank you for answering. But, how do I find out these principal minors. For a 3X3 matrix, I find them by removing the last columns and rows, and then the first two columns and rows and finally the first two columns and rows. How does it work for a 4 X 4 matrix? – WorldGov Mar 23 '18 at 15:27
1

@WorldGov for a 4-by-4 matrix for the minor of order 3 we need to eliminate the i^th row and the i^th column for i=1,2,3,4 thus we find 4 minors of order 3. For the minors of order 2 we need to eliminate 2 rows and 2 corresponding columns with $(i,j)=(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)$ thus we find 6 minors of order 2 and so on. – user Mar 23 '18 at 15:36
That helped, thank you! – WorldGov Mar 23 '18 at 15:38
@WorldGov I'm happy for that! You are welcome! Bye – user Mar 23 '18 at 15:39

score 0 · Answer 2 · answered Mar 21 '18 at 11:12

0

The principal minors of a square matrix are just the deterimants of the corresponding submatrices. Wikipedia describes it very well, see Minor.

answered Mar 21 '18 at 11:12

flawr

2 Answers2