Properties Of Determinants PDF

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Properties Of Determinants...

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Properties of Determinants 1. det(I) = 1 and det([0]) = 0.

2. det(AB) = det(A) det(B)

3. The determinant of a permutation matrix or if elementary, an elementary type I matrix.

If Permutation matrix P exchanges k pairs of rows, then det(P) = (-1)

4. The determinant of a type II elementary matrix (i)

(ii)

Multi-Linear or Linear in Rows or Row-wise Linear

If matrix A has two identical rows (or columns) then det(A) = 0.

7. If a matrix has a row (or column) of zeros then det(A) = 0

8. The determinant of a type III elementary matrix = 1.

9. The determinant of a diagonal matrix is the product of the diagonal elements.

10. The determinant of an upper or lower triangular matrix is the product of the diagonal elements...