For a linear program with standard form as follows
$$\begin{align*} \text{minimize }& \transpose{ \b{c}}\b{x} \br \text{subject to }& \b{A} \b{x} = \b{b} \br & \b{x} \geq \b{0} \end{align*}$$
where $\rank{ \b{A}} = m$.
Let $\b{A} = [\b{B}, \b{D}]$, where $\rank{\b{B}} = m$, $\b{B} $ is nonsingular.
Let $\b{x_B} = \inv{ \b{B}} \b{b} \in \R^m.$
We call ${\Vcw{ \b{x}_\b{B}}{ \b{0}}}$ a basic solution to $\b{Ax} = \b{b} $ with respect to the basis $\b{B} $.
We refer to the components of the vector $\b{x_B} $ as basic variables and the columns of $\b{B} $ as basic columns.
If some of the basic variables are zero, the basic solution is said to be degenerate basic solution.
A vector $\b{x} $ satisfying $\b{Ax}=\b{b}, \b{x} \geq \b{0} $ is said to be a feasible solution.
A feasible solution that is also basic is called a basic feasible solution.
If the basic feasible solution is a degenerate basic solution, then it is called a degenerate basic feasible solution.