scalars's Usage Examples:

While the components of vectors and tensors are in general altered under Lorentz transformations, Lorentz scalars remain unchanged.

Every quaternion algebra becomes a matrix algebra by extending scalars (equivalently, tensoring with a field extension).

Replacing the field of scalars by a commutative ring leads to the more general notion of.

generalizes the dot product to abstract vector spaces over a field of scalars, being either the field of real numbers R {\displaystyle \mathbb {R} }.

Objects that tensors may map between include vectors and scalars, and even other tensors.

Extension of scalars has numerous applications, as discussed in extension of scalars: applications.

{\displaystyle S} such that a S ⊆ S {\displaystyle aS\subseteq S} for all scalars a {\displaystyle a} satisfying | a | ≤ 1.

More complicated scalarsScalars may also be constructed from the tensors and vectors, from the contraction of tensors (such as F_{\mu\nu}F^{\mu\nu}), or combinations of contractions of tensors and vectors (such as g_{\mu\nu}x^{\mu}x^{\nu}).

Since scalars mostly may be.

Restriction of scalars changes S-modules into R-modules.

In the language of bialgebras, scalars are the unit, while.

may be added together and multiplied ("scaled") by numbers, called scalars.

Indeed, geometrically speaking, it is a null geodesic congruence with vanishing optical scalars.

Synonyms:

variable, variable quantity,

Antonyms:

invariable, consistent, constant,