Coordinate Systems From Non-Standard Bases | Definitions + Visualization

We've all used the standard coordinate system where (x,y) means x to the right and y up. However, for any subspace and a basis of that subspace, we can define a coordinate system. The same vector can thus be written in multiple coordinate systems. We describe what exactly we mean by this, introduce some new notation for it (since now we have to keep track of multiple coordinate systems), and visualize it geometrically.
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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati.
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