Non-square matrix with a sub-matrix of zeros: finding determinant

111 Views Asked by At

I'm looking at controllability matricies and determining if they are full rank.

One example has a non-square (4 x 8) controllability matrix (A|C) where A = (4x4) and C = zeros(4x4). To find the determinant, the question ignores the zero sub-matrix (C) and finds the determinant of A (the non-zero sub matrix).

Controllability matrix

Can anyone explain why this is possible? Thanks!