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It then states that, "affine independence of an n-family (x_{1},...,x_{n}) is equivalent to linear independence of one/all of the (n-1)-families:

[tex](x_{1}-x_{i},...,x_{i-1}-x_{i},x_{i+1}-x_{i},...,x_{n}-x_{i})[/tex].

I'm not immediately seeing this connection, if someone would be able to help explain it to me or send me a link so that I could understand it better, that would help. I have checked Wikipedia, MathWorld, etc. already.

Thank you very much,

-Caramon