INTEGRATION WORKSHOP 2007: LINEAR ALGEBRA LECTURE PLAN
Sheldon Axler, William C. Brown · 2007
1.2. Linear Transformations. Definitions of linear transformation, and its image and kernel. Correspondence between linear transformations and matrices, null space and column space. Gaussian elimination, reduced row echelon form, and rank. The Rank-Nullity Theorem. Solving linear systems. 1.3. Dual Spaces. Definition of the dual space V ∗ of a vector space V , and the dual basis. If V is finite dimensional, V is non-canonically isomorphic to V ∗, and V is canonically isomorphic to V ∗∗.