7.1. Matrix Properties

Determinant of a matrix:

> det(matrix(c(1:4), nrow=2))
[1] -2

The rank of a matrix can be found through its QR decomposition:

> m <- matrix(c(1,2,3, 2,4,6, 3, 3, 3), nrow=3)
> qr(m)$rank
[1] 2
> det(m)
[1] 0

Trace of a square matrix:

> A <- matrix(c(1, 2, -1, 3, -6, 9, -1, 2, 1), nrow=3)
> A
     [,1] [,2] [,3]
[1,]    1    3   -1
[2,]    2   -6    2
[3,]   -1    9    1
> sum(diag(A))
[1] -4