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...f this approach uses points, vectors and [[scalar product]] (called also [[dot product]] or [[inner product]]) of vectors without mentioning linear and affine spa

where the dot indicates a [[dot product]] between the vectors.

...f this approach uses points, vectors and [[scalar product]] (called also [[dot product]] or [[inner product]]) of vectors without mentioning linear and affine spa

.... (1), which is manifestly antisymmetric under interchange of labels (the dot product does not change, the vector '''r'''₁₂ changes sign). We will sho

Orthogonality can be verified by showing that the vector [[dot product]] is zero. The unit magnitude of these vectors is a consequence of [[#Eq. 1 as can be verified by taking the dot product with the unit vectors '''u'''_t(''s'') and '''u'''_n(''

...ub>R</sub> at time ''t'' (as can be verified by noticing that the vector [[dot product]] with the radial vector is zero) and pointing in the direction of travel.

Introducing the [[dot product]], we may write where the [[dot product]] of '''&mu;''' with itself is introduced.

and writing the [[dot product]]s as squares,

...g tasks that tend to require the same operation (for example, a sum or a [[dot product]]) to be performed on a large set of data. Some classic examples of these