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I can't understand the essence of basis in simplex method. What I know that in simplex method each time from Corner Point Feasible (CPF) solution we go in the direction of the axis with higher coefficient (assume we are maximizing objective function). It is all good while our feasible region is bounded by lines parallel to axes. But simplex method works when feasible region is bounded by line with acute angle $\alpha$ between the line and axis, where CPF solution lies on this line. But to go to this CP I need to move not only in the direction of one axis but another one too. For example moving from $(x_1;x_2)=(0;0)$ to $(0;6)$ is easy just move along $x_2$ axis. The same with moving to $(2;6)$ from $(0;6)$ — just move along $x_1$. But what if I need to move to $(2;7)$ from $(0;6)$?

So in my understanding changing basis it is some kind of changing "Point of view" so that CP becomes reachable along only one axis. I feel confused. Please clarify it to me. What does basis tell me about?

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    Do you have any familiarity with linear algebra? It seems like this is the same as the linear-algebraic notion. – 2017-02-26
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    @lan, yes. For my understanding, basis - is the set of vectors, from which all other vectors can be generated. And no for each vector there is only one way to be obtained, I mean unique linear combination. But how is it related to simplex method? Where can I see the intiution behind this? – 2017-02-26
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    @lan, **Update** And for each vector there is only one way to be obtained, I mean unique linear combination. – 2017-02-26

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