Triple product property information

In abstract algebra, the triple product property is an identity satisfied in some groups. Let G {\displaystyle G} be a non-trivial group. Three nonempty...

scalar triple product and, less often, the vector-valued vector triple product. The scalar triple product (also called the mixed product, box product, or...

In mathematics, the Jacobi triple product is the mathematical identity: ∏m=1∞(1−x2m)(1+x2m−1y2)(1+x2m−1y2)=∑n=−∞∞xn2y2n,{\displaystyle \prod _{m=1}^{\infty...

\theta }{2}}={\frac {1+\tan ^{2}\theta }{2\tan \theta }}} Formulae for triple angles. sin ⁡ ( 3 θ ) = 3 sin ⁡ θ − 4 sin 3 ⁡ θ = 4 sin ⁡ θ sin ⁡ ( π 3...

} The vector triple product is the cross product of a vector with the result of another cross product, and is related to the dot product by the following...

There are two ternary operations involving dot product and cross product. The scalar triple product of three vectors is defined as a ⋅ ( b × c ) = b...

A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), a well-known...

context, by utilising triples of subsets of finite groups which satisfy a disjointness property called the triple product property (TPP). They also give...

⋀3(R3). The scalar coefficient is the triple product of the three vectors. The cross product and triple product in three dimensions each admit both geometric...

and triple-product properties and by noting that for groups, left and right inverses always coincide. Intuitively, because of the cross products, each...

A material property is an intensive property of a material, i.e., a physical property or chemical property that does not depend on the amount of the material...

Jacobi theta functions, while capturing their general properties. In particular, the Jacobi triple product takes on a particularly elegant form when written...

term originated as an abstraction of the sequence: single, couple/double, triple, quadruple, quintuple, sextuple, septuple, octuple, ..., n‑tuple, ..., where...

degradation; double-base and triple-base propellants tend to deteriorate more slowly.: 313  To neutralize the decomposition products, which could otherwise...

identity is a property of a binary operation that describes how the order of evaluation, the placement of parentheses in a multiple product, affects the...

The Universal Product Code (UPC or UPC code) is a barcode symbology that is used worldwide for tracking trade items in stores. The chosen symbology has...

product, which generalizes the cup product. This is a higher order cohomology operation, which is only partly defined (only defined for some triples)...

acids, thus dissolving them. Its hydrogen bonding causes its many unique properties, such as having a solid form less dense than its liquid form, a relatively...

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...

Δ r i ) ) ] …  vector triple product = − [ ( ω × Δ r i ) ( ω ⋅ Δ r i ) − Δ r i ( Δ r i ⋅ ( ω × ω ) ) ] …  scalar triple product = − [ ( ω × Δ r i ) (...

This form of the Pythagorean theorem is a consequence of the properties of the inner product: ‖ v + w ‖ 2 = ⟨ v + w ,   v + w ⟩ = ⟨ v ,   v ⟩ + ⟨ w ,  ...

industrial and commercial products including, among (many) others: plastics, synthetic rubber, organic adhesives, and various property-modifying petroleum additives...