I just begun with linear programming. Given an objective function $z$ and certain restrictions defined by $Ax = b$, we got to find the values necessary to maximise or minimise that function's output... using the method "simplex".
First I have a definition for "canonical linear program". One of its points says:
The $m$ canonical vectors $e_1,e_2,...,e_m$ of $\mathbb{R}^m$ are columns in $A$, in some order. The variables associated with such columns are called basic variables.
Nice, so the canonical vectors are columns in $A$... but what are canonical vectors...?
This is followed by an example:
$$\begin{cases} -6x_1 + \color{red}{0} + \color{red}{x_3}-2x_4+2x_5=6 > \\ -3x_1+\color{red}{x_2}+\color{red}{0}+6x_4+3x_5=15 \end{cases}$$
The canonical vectors are the columns 2 and 3.
Okay. I only see two particular properties here: the columns only have one non-null term, and they also have a coefficient of 1. Is that what a canonical vector is?
$\endgroup$ 2 Reset to default
