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-