# bases

(2.7 hours to learn)

## Summary

A basis is a set of linearly independent vectors that define a coordinate system for a vector space, where the basis vectors span the entire vector space (meaning that any vector in this space can be represented as a linear combination of the basis vectors).

## Context

This concept has the prerequisites:

- subspaces (A basis is a way of representing a subspace.)

## Core resources (read/watch one of the following)

## -Free-

## -Paid-

→ Linear Algebra Done Right

A textbook for a second course in linear algebra, with mathematical generalizations of the basic concepts.

Location:
Chapter 2, "Finite-dimensional vector spaces," pages 21-34

Additional dependencies:

- vector spaces

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 4.3, "Linear independence, basis, and dimension," pages 156-168

Additional dependencies:

- linear systems as matrices

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Wikipedia

→ MIT Open Courseware: Linear Algebra (2011)

Videos for an introductory linear algebra course focusing on numerical methods.

Additional dependencies:

- column space and nullspace
- Gaussian elimination

→ A First Course in Linear Algebra (2012)

A linear algebra textbook with proofs.

Additional dependencies:

- Gaussian elimination
- complex vectors and matrices

## -Paid-

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Section 3.5, "Independence, basis, and dimension," pages 168-176

Additional dependencies:

- Gaussian elimination

## See also

-No Additional Notes-