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The definition of a "vector" in physics (including both polar vectors and pseudovectors) is more specific than the mathematical definition of "vector" (namely, any element of an abstract vector space). Under the physics definition, a "vector" is required to have components that "transform" in a certain way under a proper rotation: In particular ...
In physics, the Pauli–Lubanski pseudovector is an operator defined from the momentum and angular momentum, used in the quantum-relativistic description of angular momentum.
A pseudoscalar also results from any scalar product between a pseudovector and an ordinary vector. The prototypical example of a pseudoscalar is the scalar triple product , which can be written as the scalar product between one of the vectors in the triple product and the cross product between the two other vectors, where the latter is a ...
The vector space of matrices over is denoted by . For A ∈ K m × n {\displaystyle A\in \mathbb {K} ^{m\times n}} , the transpose is denoted A T {\displaystyle A^{\operatorname {T} }} and the Hermitian transpose (also called conjugate transpose ) is denoted A ∗ {\displaystyle A^{*}} .
As it does not change at all, the Levi-Civita symbol is, by definition, a pseudotensor. As the Levi-Civita symbol is a pseudotensor, the result of taking a cross product is a pseudovector, not a vector. [5] Under a general coordinate change, the components of the permutation tensor are multiplied by the Jacobian of the transformation matrix ...
In particle physics, the axial current, also denoted the pseudo-vector or chiral current, is the conserved current associated to the chiral symmetry or axial symmetry of a system. Origin [ edit ]
Two quite different mathematical objects are called a pseudotensor in different contexts. The first context is essentially a tensor multiplied by an extra sign factor, such that the pseudotensor changes sign under reflections when a normal tensor does not. According to one definition, a pseudotensor P of the type (,) is a geometric object whose components in an arbitrary basis are enumerated ...
In convex analysis and the calculus of variations, both branches of mathematics, a pseudoconvex function is a function that behaves like a convex function with respect to finding its local minima, but need not actually be convex.