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

The triple product rule, known variously as the cyclic chain rule, cyclic relation, cyclical rule or Euler's chain rule, is a formula which relates partial...

} 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...

In mathematics, the Jacobi triple product is the mathematical identity: ∏ m = 1 ∞ ( 1 − x 2 m ) ( 1 + x 2 m − 1 y 2 ) ( 1 + x 2 m − 1 y 2 ) = ∑ n = − ∞...

space Exterior product or wedge product Multiplication of vectors: Dot product Cross product Seven-dimensional cross product Triple product, in vector calculus...

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...

Triple product is a ternary operation on vectors. It may also mean: Jacobi triple product, an identity in number theory Triple product rule, a calculus...

useful figure of merit is the triple product of density, confinement time, and plasma temperature T. The triple product also has a minimum required value...

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...

\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...

cross product of two vectors is a pseudovector instead of a vector (see below). The scalar triple product (also called the box product or mixed triple product)...

⋀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...

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 ) (...

Triple Product Marked in High-βp H-mode Plasmas". Archived from the original on 2013-01-06. "Measuring Progress in Fusion Energy: The Triple Product"...

three-dimensional vectors, this is equal to the square of the scalar triple product det [ A , B , C ] = | A , B , C | {\displaystyle \det[\mathbf {A} ,\mathbf...

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...

denotes the scalar triple product of the three vectors and a → ⋅ b → {\displaystyle {\vec {a}}\cdot {\vec {b}}} denotes the scalar product. Care must be taken...

and hence is a Lie algebra g0. Any Jordan triple system is a Lie triple system with respect to the product [ u , v , w ] = { u , v , w } − { v , u , w...

)+H^{*}(\Gamma )[w]).} So the Massey product can be regarded as a function defined on triples of classes such that the product of the first or last two is zero...

mathematics, for a sequence of complex numbers a1, a2, a3, ... the infinite product ∏ n = 1 ∞ a n = a 1 a 2 a 3 ⋯ {\displaystyle \prod _{n=1}^{\infty...

\mathbf {x} \times \mathbf {y} =-\mathbf {y} \times \mathbf {x} } Scalar triple product: x ⋅ ( y × z ) = y ⋅ ( z × x ) = z ⋅ ( x × y ) {\displaystyle \mathbf...

while capturing their general properties. In particular, the Jacobi triple product takes on a particularly elegant form when written in terms of the Ramanujan...

basic algebraic operations consist of: Also commonly used are the two triple products: Vector calculus studies various differential operators defined on...

the product of two cubes, {4,3} × {4,3}. In geometry of 6 dimensions or higher, a triple product is a polytope resulting from the Cartesian product of...

, then ( x , y , z ) {\displaystyle (x,y,z)} may denote the scalar triple product.[citation needed] See also [□,□,□] in § Square brackets. (□, ..., □)...

× 3 inverse can be expressed concisely in terms of the cross product and triple product. If a matrix A = [ x 0 x 1 x 2 ] {\displaystyle \mathbf {A}...

Box product may refer to: The scalar triple product of three vectors A cartesian product of topological spaces equipped with the box topology The cartesian...

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...

}}\times \mathbf {r} } The expression inside the integral is a scalar triple product F ⋅ d θ × r = r × F ⋅ d θ {\displaystyle \mathbf {F} \cdot \mathrm {d}...

society and culture. Digital media platforms like YouTube work through a triple-product business model in which platforms provide information and entertainment...