# Vector Independence, Span, Basis, and Dimension

Taught by OCW
• Currently 4.0/5 Stars.
12467 views | 2 ratings
Part of video series
Lesson Summary:

In this lecture, we learn about vector independence, span, basis, and dimension. We are introduced to the definitions of linear independence and span, and we see how they relate to each other. A set of vectors is independent if no combination of them gives the zero vector, and they span a space if all their linear combinations fill up the entire space. The concept of a basis is also introduced, which is a set of vectors that is both independent and spans the space. The lecture includes examples in two and three-dimensional space to demonstrate these concepts.

Lesson Description:

Vector Independence, Span, Basis, and Dimension -- Lecture 9. Learn when vectors are independent or dependent, what a vector span is, what a basis is, and how to find the dimension.

Gilbert Strang, 18.06 Linear Algebra, Spring 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed November 19, 2008). License: Creative Commons BY-NC-SA.
• 