scalar product
and this generalizes naturally to higher dimensions.
The scalar product has the following properties:
(i) u·v = v·u.
(ii) For non-zero vectors u and v, u·v = 0 if and only if u is perpendicular to v.
(iii) u·u = |u|2; the scalar product u·u may be written u2.
(iv) u·(v+w) = u·v+u·w, the distributive law.
(v) u·(kv) = k(u·v).
The length |u| of a vector can be defined in terms of the scalar product from (iii). Further, the angle θ between u and v can be defined by
This uniquely defines an angle θ in the range 0 ≤ θ ≤ π by the Cauchy-Schwarz inequality.
- solid of revolution
- solidus
- soluble group
- solution
- solution of triangles
- solution set
- solvable by radicals
- solvable group
- sorting algorithms
- source
- source
- source
- space
- space-filling curve
- space–time
- span
- spanning set
- spanning tree
- sparse matrix
- Spearman's rank correlation coefficient
- special function
- special linear group
- special relativity
- spectral theorem
- spectrum