Dot Product

In mathematics, the dot product, or scalar product (or sometimes inner product in the context of Euclidean space), is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. This operation can be defined either algebraically or geometrically. Algebraically, it is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the magnitudes of the two vectors and the cosine of the angle between them. The name "dot product" is derived from the centered dot " " that is often used to designate this operation; the alternative name "scalar product" emphasizes the scalar (rather than vector) nature of the result.

In three dimensional space, the dot product contrasts with the cross product, which produces a vector as result. The dot product is directly related to the cosine of the angle between two vectors in Euclidean space of any number of dimensions.

Read more about Dot Product:  Definition, Properties, Triple Product Expansion, Physics

Other articles related to "dot product, product, products":

Dot Product - Generalizations - Tensors
... The inner product between a tensor of order n and a tensor of order m is a tensor of order n + m − 2, see tensor contraction for details ...
ARB (GPU Assembly Language) - Details - ARB Assembly Instructions
... value ADD - add ARL - address register load DP3 - 3-component dot product DP4 - 4-component dot product DPH - homogeneous dot product DST - distance vector EX2 - exponential base 2 EXP ...
Synchronous Code Division Multiple Access - Code Division Multiplexing (Synchronous CDMA)
... Vectors can be multiplied by taking their dot product, by summing the products of their respective components (for example, if u = (a, b) and v = (c, d ... If the dot product is zero, the two vectors are said to be orthogonal to each other ... Some properties of the dot product aid understanding of how W-CDMA works ...
Trace Diagram - Examples - 3-Vector Diagrams
... It can be shown that the cross product and dot product of 3-dimensional vectors are represented by In this picture, the inputs to the function are shown as vectors in yellow boxes at the bottom of the diagram ... The cross product diagram has an output vector, represented by the free strand at the top of the diagram ... The dot product diagram does not have an output vector hence, its output is a scalar ...

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