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.
2026-04-02 15:05:59.1775142359
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How many leading principal minors are there for a $4 \times 4$ matrix?
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the first order leading principal minors is a11. the second order leading principal minors is a11*a22-a21*a12. the third order leading principal minors is the determinant of the original matrix after deleting the last rows and columns. the first order leading principal minors is determinant of the original matrix A.
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.