This online Dot Product Calculator performs calculation of the dot product (or scalar product) of two vectors defined in a space of arbitrary dimension. You can paste to the respective fields of the calculator the vectors components copied from a spreadsheet or csv-file or input manually using comma, space or enter as separators.
Dot Product of Vectors
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. It is often called the inner product (or rarely projection product) of Euclidean space.
In linear algebra the dot product of two vectors \(\mathbf{x} = \{ { x }_{ 1 },{ x }_{ 2 },…,{ x }_{ n }\}\) and \(\mathbf{y} = \{ { y }_{ 1 },{ y }_{ 2 },…,{ y }_{ n }\}\) is defined as:
$$\mathbf{x}\cdot \mathbf{y}=\sum _{ i=1 }^{ n }{ { x }_{ i }{ y }_{ i } },$$
where \(n\) is the dimension of the vector space.
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