The meaning of notation $[A : B]$ when $A$ and $B$ are matrices While reading an article [1], I encountered notation that I couldn't decipher: $[A : B]$, where $A$ and $B$ are both $n \times n$ real matrices. The following statement was also given (if that helps): > If $[A : B]$ has full rank $a \in \ker A^T$ and $a \in \ker B^T$ implies $a = 0$. What does $[A : B]$ mean? * * * [1]: Jesús Rodríguez and Kristen Kobylus Abernathy: On the solvability of nonlinear boundary value problems

That's an augmented matrix. It's the $n\times2n$ matrix you get from putting $A$ and $B$ next to one another and interpret it as a single matrix.