physics, the algebra of physical space (APS) is the use of the Clifford or geometric algebra Cl3,0(R) of the three-dimensional Euclidean space as a model...

while Dirac algebra uses complex number scalars. The STA spacetime split is similar to the algebra of physical space (APS, Pauli algebra) approach. APS...

geometric algebras applied in physics include the spacetime algebra (and the less common algebra of physical space) and the conformal geometric algebra. Geometric...

Clifford algebra is an algebra generated by a vector space with a quadratic form, and is a unital associative algebra with the additional structure of a distinguished...

introduced. In geometric algebra (GA) these are multivectors, which sometimes follow Ricci calculus. In the Algebra of physical space (APS), also known as...

The Dirac equation in the algebra of physical space uses a Clifford algebra over the real numbers, a type of geometric algebra. As mentioned above, the...

analysis, a branch of mathematics, an operator algebra is an algebra of continuous linear operators on a topological vector space, with the multiplication...

idea of using the Pauli matrices as basis vectors is employed in the algebra of physical space, an example of a Clifford algebra. In spacetime algebra, another...

{\displaystyle \mathbb {C} } ) ≅ Spin(3,1). Anyon Dirac equation in the algebra of physical space Eigenspinor Einstein–Cartan theory Projective representation Pure...

variety of different formulations of the algebra to be given, as noted in the examples below. Poisson algebras occur in various settings. The space of real-valued...

examples of nontrivial physical phenomena he believes arose from the mathematical tools employed and not from the intrinsic properties of physical reality...

library, where emphasis is placed on clear understanding of algorithms. Many computer algebra systems (listed above) can also be used for numerical computations...

Hausdorff space. C*-algebras were first considered primarily for their use in quantum mechanics to model algebras of physical observables. This line of research...

K[x]_{(x-c)}} of the local ring at (x-c), a point together with a neighborhood around it. Algebraic varieties also have a well-defined notion of tangent space called...

needed] The term algebraic coding theory denotes the sub-field of coding theory where the properties of codes are expressed in algebraic terms and then...

of CAPS (complexified algebra of physical space), which is Clifford algebra C l ( 3 , C ) {\displaystyle Cl(3,\mathbb {C} )} . Since the linear space...

and in that context goes by the name Algebra of physical space (not to be confused with the Spacetime algebra, which is 16-dimensional.) H.S.M. Coxeter:...

units of length (e.g., metre). In algebraic geometry there are several structures that are one-dimensional spaces but are usually referred to by more...

viewed as the application of linear algebra to function spaces. Linear algebra is also used in most sciences and fields of engineering, because it allows...

equivalence of deterministic and nondeterministic finite automata. In the 1960s, a body of algebraic results known as "structure theory" or "algebraic decomposition...

equation Laws of science Defining equation (physical chemistry) List of equations in classical mechanics Table of thermodynamic equations List of equations...

particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and...

Hamilton in 1843 and applied to mechanics in three-dimensional space. The algebra of quaternions is often denoted by H (for Hamilton), or in blackboard...

In mathematics, a Lie algebra (pronounced /liː/ LEE) is a vector space g {\displaystyle {\mathfrak {g}}} together with an operation called the Lie bracket...

number of different settings in physics and applied mathematics. Examples of the "collection of equations" D {\displaystyle D} include algebraic equations...

coordinate vector space. Many vector spaces are considered in mathematics, such as extension fields, polynomial rings, algebras and function spaces. The term...

numerical integration of ordinary differential equations (ODEs) and differential algebraic equations (DAEs), to be used. A large number of integration routines...

theory to define the probability space: Given any set Ω {\displaystyle \Omega \,} (also called sample space) and a σ-algebra F {\displaystyle {\mathcal {F}}\...

Poisson bracket. The Poisson bracket gives the space of functions on the manifold the structure of a Lie algebra. If F and G are smooth functions on M then...

linear algebra and numerical solution of partial differential equations Stochastic methods, such as Monte Carlo methods and other representations of uncertainty...