When learning optimization, I heard the two related concepts on linear algebra:
linearly independent and affinely independent. The definition itself is pretty clear. But how to understand their differences and relationship?
2026-05-17 07:20:33.1779002433
the differences and relationship between linear independent and affinely independent
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One difference between an affine space and a vector space is that an affine space does not have an origin point. If you fix one, then you can regard the affine space as a vector space. So in your definition, the additionnal vector $x^1$ can treated as a choice of origin.