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 ...

... 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 ...

... 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 ...

... 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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“Labor is work that leaves no trace behind it when it is finished, or if it does, as in the case of the tilled field, this *product* of human activity requires still more labor, incessant, tireless labor, to maintain its identity as a “work” of man.”

—Mary McCarthy (1912–1989)