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先给出标准形式的线性规划问题：

Let's start with the linear programming problem in standard form:

可行解 满足上述约束条件(1.7)和(1.8)的解X，称为线性规划问题的可行解。全部可行解的集合称为可行域。

Feasible solution A solution X that satisfies the above constraints (1.7) and (1.8) is called a feasible solution to a linear programming problem. The set of all feasible solutions is called a feasible domain.

最优解 使目标函数(1.6)达到最大值的可行解称为最优解。

Optimal solution A feasible solution that maximizes the objective function (1.6) is called the optimal solution.

基 设A为约束方程组(1.7)的m×n阶系数矩阵(设n>m),其秩为m,B是矩阵A中的一个m×m阶的满秩子矩阵,称B是线性规划问题的一个基。不失一般性,设

Let base A be a matrix of coefficients of order m×n (let n>m) of the system of constraint equations (1.7), whose rank is m, and B is a full-rank submatrix of order m ×m in matrix A, and B is said to be a basis for linear programming problems. Without losing the generality, set

B中的每一个列向量

Each column vector in B

称为基向量,与基向量 P对应的变量;称为基变量。线性规划中除基变量以外的变量称为非基变量。

called the basis vector, the variable corresponding to the basis vector P; This is called a base variable. Variables other than base variables in linear programming are called non-base variables.

基解 在约束方程组(1.7)中,令所有非基变量

Basis solution In the system of constraint equations (1.7), let all non-basis variables

又因为有|B|≠0，根据克莱姆规则，由m个约束方程可解出m个基变量的唯一解

And because there is |B|≠0, according to Clem's rule, the only solution of m basis variables can be solved from m constraint equations

将这个解加上非基变量取0的值有

Adding this solution to the non-basis variable takes the value of 0

,称X为线性规划问题的基解。在基解中变量取非零值的个数不大于方程数 m,故基解的总数不超过的个数为：

, which is called the basis solution of the linear programming problem. The number of variables with nonzero values in the fundamental solution is not greater than the number of equations m, so the total number of fundamental solutions does not exceed is:

基可行解 满足变量非负约束条件(1.8)的基解称为基可行解。

Basis feasible solution A fundamental solution that satisfies the variable non-negative constraint (1.8) is called a basis feasible solution.

可行基 对应于基可行解的基称为可行基。

Feasible Basis The basis corresponding to the feasible solution of the basis is called the feasible basis.

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翻译：百度翻译