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alternate case: multiplication of vectors

Vector algebra relations
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See also: Vector calculus identities The relations below apply to vectors in a three-dimensional Euclidean space. Some, but not all of them, extend toLorentz scalar (628 words) [view diff] exact match in snippet view article find links to article

Lorentz transformation. A Lorentz scalar may be generated from multiplication of vectors or tensors. While the components of vectors and tensors are inCommutative property (1,845 words) [view diff] exact match in snippet view article find links to article

addition and multiplication of complex numbers, addition and scalar multiplication of vectors, and intersection and union of sets. Concatenation, the act ofSubalgebra (481 words) [view diff] exact match in snippet view article find links to article

ring or field is a vector subspace which is closed under the multiplication of vectors. The restriction of the algebra multiplication makes it an algebraQuaternionic polytope (223 words) [view diff] exact match in snippet view article find links to article

quaternions are non-commutative, a convention must be made for the multiplication of vectors by scalars, which is usually in favour of left-multiplicationPolar sine (479 words) [view diff] exact match in snippet view article find links to article

of row-exchanging in the determinant: Invariance under scalar multiplication of vectors The polar sine does not change if all of the vectors v1, ..., vnComplex spacetime (822 words) [view diff] exact match in snippet view article find links to article

field). To "complexify" a space means extending ordinary scalar multiplication of vectors by real numbers to scalar multiplication by complex numbers. ForVectors in three-dimensional space (278 words) [view diff] exact match in snippet view article find links to article

displacements including these sections: Introduction, Scalar multiplication of vectors, Addition and subtraction of vectors, Displacements in EuclideanLinear algebra (6,345 words) [view diff] exact match in snippet view article find links to article

coordinate n-space Fn. Under this identification, addition and scalar multiplication of vectors in V correspond to addition and scalar multiplication of theirClassical Hamiltonian quaternions (4,280 words) [view diff] exact match in snippet view article find links to article

the numerator times the reciprocal of the denominator. Since multiplication of vectors is not commutative, the order cannot be changed in the following