Linear maps

Abstract

As we have discussed in the lecture on ”What is Linear Algebra?” one of the main goals of linear algebra is the characterization of the solutions to the set of m linear equations in n unknowns x1, . . . , xn a11x1 + · · · + a1nxn = b1 .. .. .. am1x1 + · · · + amnxn = bm, where all coefficients aij and bi are in F. Linear maps and their properties that we are about to discuss give us a lot of insight into the characteristics of the solutions.