Sage SUTH4 Sage Under The Hood, Round 4

We finally have enough theorems to understand how Sage creates and manages linear transformations. With a choice of bases for the domain and codomain, a linear transformation can be represented by a matrix. Every interesting property of the linear transformation can be computed from the matrix representation, and we can convert between representations (of vectors and linear transformations) with change-of-basis matrices, similarity and matrix multiplication.

So we can understand the theory of linear algebra better by experimenting with the assistance of Sage, and the theory of linear algebra helps us understand how Sage is designed and functions. A virtuous cycle, if there ever was one. Keep it going.