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In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors. For example, 21 is the product of 3 and 7 (the result of multiplication), and x ⋅ ( 2 + x ) {\displaystyle x\cdot (2+x)} is the product of x {\displaystyle x} and ( 2 + x ) {\displaystyle ...
Given two linearly independent vectors a and b, the cross product, a × b (read "a cross b"), is a vector that is perpendicular to both a and b, [1] and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming.
The mixed-product property also works for the element-wise product. If A and C are matrices of the same size, B and D are matrices of the same size, then [7] ( A ⊗ B ) ∘ ( C ⊗ D ) = ( A ∘ C ) ⊗ ( B ∘ D ) . {\displaystyle (\mathbf {A} \otimes \mathbf {B} )\circ (\mathbf {C} \otimes \mathbf {D} )=(\mathbf {A} \circ \mathbf {C ...
In mathematics, the Lambert W function, also called the omega function or product logarithm, is a multivalued function, namely the branches of the converse relation of the function f(w) = we w, where w is any complex number and e w is the exponential function. The function is named after Johann Lambert, who considered a related problem in 1758.
In mathematics, the dot product or scalar product is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used.
The Physical Review submission instructions recommend against expressions of the form a / b / c; more explicit expressions (a / b) / c or a / (b / c) are unambiguous. [16] 6÷2 (1+2) is interpreted as 6÷ (2× (1+2)) by a fx-82MS (upper), and (6÷2)× (1+2) by a TI-83 Plus calculator (lower), respectively.
In mathematics, the tensor product of two vector spaces V and W (over the same field) is a vector space to which is associated a bilinear map that maps a pair (,), , to an element of denoted . An element of the form v ⊗ w {\displaystyle v\otimes w} is called the tensor product of v and w .
The product rule can be generalized to products of more than two factors. For example, for three factors we have d ( u v w ) d x = d u d x v w + u d v d x w + u v d w d x . {\displaystyle {\frac {d(uvw)}{dx}}={\frac {du}{dx}}vw+u{\frac {dv}{dx}}w+uv{\frac {dw}{dx}}.}
Microsoft Math contains features that are designed to assist in solving mathematics, science, and tech-related problems, as well as to educate the user. The application features such tools as a graphing calculator and a unit converter. It also includes a triangle solver and an equation solver that provides step-by-step solutions to each problem.
The cardinality of a set is the number of elements of the set. For example, defining two sets: A = {a, b} and B = {5, 6}. Both set A and set B consist of two elements each. Their Cartesian product, written as A × B, results in a new set which has the following elements: A × B = { (a,5), (a,6), (b,5), (b,6)}.