Some notes about matrices

1 Linear algebra and geometry on R, C If m, n are positive integers, we shall denote by L(R,R) the space of reallinear mappings from R to R, and by L(C,C) the space of complexlinear mappings from C to C. In the special case where m = n, we may simply write L(R), L(C), respectively. Also when m = n, we write I for the identity mapping on R or C, as appropriate. Using the standard basis for real and complex Euclidean spaces, linear transformations can be identified with matrices in the usual manner. Let