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?

Answer 1

We have

• $4 =\binom{4}{1}$ principal minor of order $1$
• $6 =\binom{4}{2}$ principal minor of order $2$
• $4 =\binom{4}{3}$ principal minor of order $3$

Answer 2

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