Advanced Linear Algebra, Lecture 1.5: Dual vector spaces

Advanced Linear Algebra, Lecture 1.5: Dual vector spaces The dual of a vector space X over K is the space X' of all linear scalar functions from X to K, which are also called co-vectors or dual vectors. When dim(X)=n is finite, then X and X' are isomorphic. We can think about vectors as length-n column vectors, and dual vectors as length-n row vectors. The function l(x) is simply the scalar product of these, so we can denote it as (l,x)=l(x). We conclude with an example of an infinite-dimensional vector space that has a dual vector that is not of this form. Course webpage: http://www.math.clemson.edu/~macaule/...