Row Cofactors of A[i,]

Returns the vector of cofactors of row i of the square matrix A. The determinant, Det(A), can then be found as M[i,] %*% rowCofactors(M,i) for any row, i.

rowCofactors(A, i)

Arguments

A

a square matrix

i

row index

Value

a vector of the cofactors of A[i,]

See also

Det for the determinant

Other determinants: Det(), adjoint(), cofactor(), minor(), rowMinors()

Author

Michael Friendly

Examples

M <- matrix(c(4, -12, -4,
              2,   1,  3,
             -1,  -3,  2), 3, 3, byrow=TRUE)
minor(M, 1, 1)
#> [1] 11
minor(M, 1, 2)
#> [1] 7
minor(M, 1, 3)
#> [1] -5
rowCofactors(M, 1)
#> [1] 11 -7 -5
Det(M)
#> [1] 148
# expansion by cofactors of row 1
M[1,] %*% rowCofactors(M,1)
#>      [,1]
#> [1,]  148