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...

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

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...

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...

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...

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:...

geometric algebras applied in physics include the spacetime algebra (and the less common algebra of physical space). Geometric calculus, an extension of GA that...

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...

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

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

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

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...

as elements of a vector space that carries a linear representation of the Clifford algebra. The Clifford algebra is an associative algebra that can be...

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

different Cartan pair gives a similar "X–Y decomposition of a single-qubit gate. Algebra of physical space Spinors in three dimensions Gamma matrices § Dirac...

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

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

being defined for a vector space and then applied pointwise to a vector field. The basic algebraic operations consist of: Also commonly used are the...

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

counterpart of velocity, which is a three-dimensional vector in space. Physical events correspond to mathematical points in time and space, the set of all of them...

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

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

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...

field of a plane wave without sources is nilpotent when it is expressed in terms of the algebra of physical space. More generally, the technique of microadditivity...

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

Source, a synchrotron X-ray source at Argonne National Laboratory Algebra of physical space, in physics Ammonium persulfate, in chemistry Apus, abbreviation...

Bachelier in 1900 and by Albert Einstein in 1905 and other physical diffusion processes in space of particles subject to random forces. Since the 1970s, the...

areas of science (computational science) as well as the mathematics of computation (for example, theoretical computer science, computer algebra, numerical...

supersymmetry algebra (or SUSY algebra) is a mathematical formalism for describing the relation between bosons and fermions. The supersymmetry algebra contains...