# 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**.
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.
The alternative name scalar product emphasizes the scalar rather than vector.
Lets get our feet wet by thinking in terms of vectors and spaces.
The first four axioms mean that v is an abelian group under addition.
Definitions of the vector dot product and vector length.

These properties may be summarized by saying that the dot product is a bilinear form. The name is derived from the centered dot that is often used to designate this operation. Then we look through what vectors and matrices are and. Linear algebra from imperial college london. Mathematics for machine learning.

The dot product is thus characterized geometrically by. 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. Elements of a vector space may have various nature. This page documents the core linear algebra tools included in dlib.