:The Parallelogram law is, in fact, a necessary and sufficient condition for the existence of a scalar product corresponding to a given norm.
32.
However, in all countries the full stop is used to indicate a dot product, i . e . the scalar product of two vectors.
33.
:: What might help is if I found a nontrivial product of scalar products identity of the kind I've mentioned, preferably a minimal one.
34.
Where parentheses ( * * ) is a scalar product and square brackets [ * * * ] is a scalar triple product, and is an imaginary unit.
35.
Of course, the sum involved are not convergent, but the trick is to use the unitary property of Fourier transform which is that it preserves scalar product:
36.
In first approximation, the energy density of the interaction between two ferromagnetic layers separated by a non-magnetic layer is proportional to the scalar product of their magnetizations:
37.
A scalar product operation not to be confused with scalar multiplication may be defined on a vector space, allowing two vectors to be multiplied to produce a scalar.
38.
The ring product inherited by this quotient is sometimes referred to as the "'Clifford product "'to differentiate it from the exterior product and the scalar product.
39.
In case of spin-particles, it is possible to find a construction that includes both a finite-dimensional representation and a scalar product that is preserved by this representation.
40.
Dense instruction coding, and extensive use of the register sets, meant that relatively few store accesses were needed for common scientific codes, such as scalar product and polynomial inner loops.
