In this video, I review the definition of basis, and discuss the notion of coordinates of a vector relative to that basis.
The properties of a basis of a subspace guarantee that a vector in that subspace can be written as a linear combination of the basis vectors in only one way. The weights in that unique linear combination are called the coordinates of the vector relative to that basis.
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We learned about how vectors can form a basis for a vector space, and we can express any vector within a vector space as a linear combination of the basis vectors. But there can be more than one set of basis vectors. What if we want to express a vector using some other basis rather than the standard basis? Well we can implement a change of basis, so let’s learn how to do that!
Script by Howard Whittle
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