Early in Chapter VS we prefaced the definition of a vector space with the comment that it was “one of the two most important definitions in the entire course.” Here comes the other. Any capsule summary of linear algebra would have to describe the subject as the interplay of linear transformations and vector spaces. Here we go.

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##### A linear transformation is given by a matrix whose columns are the images of the standard basis vectors, coordinate setting. math.la.t.lintrans.mat.basis.standard.coord