How many leading principal minors are there for a $4 \times 4$ matrix? How many leading principal minors are there for a $4 \times 4$ matrix?


Please explain in detail. I know for a $3 \times 3$ matrix.
The kth order leading principal minor is the determinant of the kth order principal
submatrix formed by deleting the last n − k rows and columns.
I think you are referring to leading principal submatrix rather than leading principal minors, which is a bit broad. If you can find for 3*3 matrix and you know how to do it, you can use the same method to find for 4*4 matrix.