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It can be tempting to reduce linear algebra to 'matrices and vectors', but there is more to it. Often times you can find a 'matrix algebra' course or something along those lines (I remember taking 'computational matrix algebra'), which really does pretty much just discuss computations with matrices and vectors. Linear algebra has more to do with the properties of vector spaces and 'linear transformations' on vector spaces—which can be represented using matrices, but there are deeper underlying concepts than the matrix computations themselves.



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