The Vector Space of Polynomials: Span, Linear Independence, and Basis

We normally think of vectors as little arrows in space. We add them, we multiply them by scalars, and we have built up an entire theory of linear algebra around these objects. However, it turns out that polynomials of degree less than or equal to n ALSO form a so called vector space; that is, they also have a vector addition and a scalar multiplication that obeys the same long list of algebraic rules as vector. This means we can do linear algebra on these polynomial vector spaces in much the same way. In this video we'll cover the standard ideas of span, linear independence, and basis, and see how these ideas from the vector space R^n extend over to the vector space of polynomials of degree less than or equal to n with real coefficients. We'll do a full example showing how to demonstrate these concepts algebraically.

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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