I need to find the limit $$ \lim_{r\to 0}{\frac{B.r}{a^*.r}}, $$ where $B$ is a $n\times n$ matrix in $C^{n\times n}$, $a$ and $r$ are vector columns in $C^n$. Vector $a^*$ is the conjugate transpose of vector $a$ and $a^*.r$ is the inner product.
Is there any analog of the L'hopital rule for vector sequences? Or how can I find this limit?