Rank-Nullity Theorem

Let $T:V -> W$ be a linear transformation between two vector spaces

Formel

$rank(T)+nullity(T)\dim(V)$
$dim(V)$ is the number of columns in $T$ .

Nullity is the dimension of the kernel: $dim(kern(T))$

If theRank is full the transformation is surjective (opens in a new tab)

If the dimension of the Kernel is 0 the transformation is Injective (opens in a new tab)