Change of basis matrix

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What is the matrix we use to convert coordinates from one basis to another?
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the video on gram schmidt orthogonalization is really helpful.. visualizing the process became easier... keep up making such content, we need more of it.. also, can you please make a similar video on linear transformation, affine subspaces and affine mappings? It is really difficult to study linear algebra without visualizing what's happening.

anubhutipriya