Before we can get to the definition of the determinant of a matrix, ... We define a transposition of two elements the permutation that switches the elements ...
We'll write σ1 = 2, σ2 = 4, σ3 = 1, σ4 = 5, and σ5 = 3. Permutation matrices. One way to look at a permutation is to treat it as a matrix itself. First, think ...
Therefore, any permutation matrix P factors as a product of row-interchanging elementary matrices, each having determinant −1. Thus the determinant of a ...
determinant of permutation matrix ... It's a well known fact that det(P)=(−1)t, where t is the number of row exchanges in the PA=LU decomposition. Can somebody ...
The determinant of a permutation matrix is either 1 or –1, because after changing rows around (which changes the sign of the determinant) a permutation matrix becomes I, whose determinant is one. Definition: the sign of a permutation, sgn(σ), is the determinant of the corresponding permutation matrix.