Matrix - Rank

The rank of a matrix is the dimension of its column space. It is denoted as $\mathrm{rank}(A)$ for a matrix $A$.

In human terms, it refers to the number of linearly independent vectors in the column space of the matrix.

More formally, we can define the rank of a matrix $A$ as follows:

$$\mathrm{rank}(A)=\dim (\mathrm{Col}(A))$$