# Linear Algebra Dot Product

### In particular the three most important objects in this part of the library are the matrix vector and rectangleall the other tools on this page are functions for manipulating these three objects.

**Linear algebra dot product**.
In mathematics the dot product is an operation that takes two vectors as input and that returns a scalar number as output.
This page documents the core linear algebra tools included in dlib.
These properties may be summarized by saying that the dot product is a bilinear form.
For example they can be sequences functions polynomials or matriceslinear algebra is concerned with properties common to all vector spaces.
The blas basic linear algebra subprograms are routines that provide standard building blocks for performing basic vector and matrix operations.

In this course on linear algebra we look at what linear algebra is and how it relates to vectors and matrices. Lets get our feet wet by thinking in terms of vectors and spaces. The dot product is thus characterized geometrically by. Linear algebra from imperial college london. Elements of a vector space may have various nature.

The alternative name scalar product emphasizes the scalar rather than vector. The dot product defined in this manner is homogeneous under scaling in each variable meaning that for any scalar a it also satisfies a distributive law meaning that. Then we look through what vectors and matrices are and. Definitions of the vector dot product and vector length. The first four axioms mean that v is an abelian group under addition.