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I did some linear algebra studies and learned how to change between foreign bases and the standard basis:
Change of basis matrix multiplied by the vector in coordinates with respect to the foreign basis equals the vector in coordinates with respect to the standard basis.
Of course, this is just changing bases while operating with vectors. Now I have a few questions:
1. What if I want to change between two different foreign bases (by foreign I just mean as opposed to the standard basis)? Is the formula still the same except you just put the foreign basis you are trying to get to in place of the standard basis in the formula I listed above?
2. How do you make a change of bases with tensors? My guess would be that you derive the basis vectors for a coordinate system, put those basis vectors in a change of basis matrix and multiply this change of basis matrix by the tensor in the basis you are trying to get away from. This should equal that same tensor in the basis you are trying to get to. Please correct me if I am wrong.
3. Where can I find a good multi linear algebra video playlist? Khan academy has linear algebra, but its playlist doesn't include multilinear algebra or tensor analysis of any sort. I found a play list on youtube, but all the videos were made private, so I can't see them.
Change of basis matrix multiplied by the vector in coordinates with respect to the foreign basis equals the vector in coordinates with respect to the standard basis.
Of course, this is just changing bases while operating with vectors. Now I have a few questions:
1. What if I want to change between two different foreign bases (by foreign I just mean as opposed to the standard basis)? Is the formula still the same except you just put the foreign basis you are trying to get to in place of the standard basis in the formula I listed above?
2. How do you make a change of bases with tensors? My guess would be that you derive the basis vectors for a coordinate system, put those basis vectors in a change of basis matrix and multiply this change of basis matrix by the tensor in the basis you are trying to get away from. This should equal that same tensor in the basis you are trying to get to. Please correct me if I am wrong.
3. Where can I find a good multi linear algebra video playlist? Khan academy has linear algebra, but its playlist doesn't include multilinear algebra or tensor analysis of any sort. I found a play list on youtube, but all the videos were made private, so I can't see them.