MATH 305 Lecture Notes - Lecture 11: Identity Matrix, Suse Linux Distributions, Simplex Algorithm
19 May 2016
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4. 3 matrix representation of the simplex method - part i. Matrix form of lp problem, basis matrix b. Note: the text book writes c as a row vector instead of a column vector. Any invertible m m square sub-matrix b of a is called a basis matrix of a. Basis matrix b is in fact the sub-matrix of a corresponding to the basic variables. For any basis matrix b, think of a as being partitioned as a= [b n], where n is the left and the cost vector c as over m (n-m) matrix which is called a non-basis matrix. Each basis matrix corresponds to a basic solution, we can partition the solution vector x where xb and cb are called the basic variable vector and basic cost vector respectively. Solution in matrix form: xb = b-1b, z = z0 + cb.
