Dual linear programme

Suppose we have a linear programme in standard form given by $A \in M_{m,n}(\mathbb{R})$, $b \in M_{m,1}(\mathbb{R})$ and $c \in M_{n,1}(\mathbb{R})$. Define the dual linear programme to be defined by $-A^T \in M_{n,m}$, $-c \in M_{n,1}(\mathbb{R})$ and $-b \in M_{m,1}(\mathbb{R})$. Where we want to solve for some $y \in M_{m,1}$ where we

$$ \max_y -b y^T \mbox{ such that } -A^Ty \leq -c.$$

Note we have added the minus signs to keep it in standard form.