Unformatted text preview: ( −→ x ) . In other words, an aFne function is the same thing as a polynomial of degree one (with no homogeneity conditions—that is, without any restriction on the constant term). Note that if φ ( −→ x ) = c + ℓ ( −→ x ) is an aFne function, then for any two vectors −→ x and −→ y , φ ( −→ y ) − φ ( −→ x ) = ℓ ( −→ y ) − ℓ ( −→ x ) = ℓ ( −→ y − −→ x ); setting △ −→ x = −→ y − −→ x , so that −→ y = −→ x + △ −→ x we can write φ ( −→ x + △ −→ x ) = φ ( −→ x ) + ℓ ( △ −→ x ) . (3.1)...
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 Fall '08
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 Calculus, Linear Algebra, Vector Space, Euclidean vector

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