# Each vector can be written uniquely as a linear combination of vectors from a given basis.

math.la.t.vsp.basis.coord.unique

# Coordinate systems

Representation (unique) of a vector in terms of a basis for a vector space yields coordinates relative to the basis; change of basis and corresponding change of coordinate matrix

##### math.la.d.vsp.basis.relative.coord
Created On
August 25th, 2017
7 years ago
Views
3
Type
Video
Language
English
Content Type
text/html; charset=utf-8

# Linear Independence and Spanning Sets - A First Course in Linear Algebra

A vector space is defined as a set with two operations, meeting ten properties (Definition VS). Just as the definition of span of a set of vectors only required knowing how to add vectors and how to multiply vectors by scalars, so it is with linear independence. A definition of a linearly independent set of vectors in an arbitrary vector space only requires knowing how to form linear combinations and equating these with the zero vector. Since every vector space must have a zero vector (Property Z), we always have a zero vector at our disposal.