Week of 
Contents 
Sections 
1/26 
Linear systems and their geometric interpretation. Matrices and vectors. The matrix form of a linear system. GaussJordan elimination. 
1.11.2 
2/2 
Matrix vocabulary. Operations on matrices. Space R^{n}. Rank of a matrix. Number of solutions of a linear system. 
1.21.3 
2/92/16 
Linear transformations from R^{m} to R^{n}. Matrix of a linear transformation. Linear transformations in a plane: scalings, projections, reflections, rotations, shears. Composition of linear transformations and matrix product. Inverse linear transformation and invertible matrices. 
2.12.4 
2/23 
Subspaces of R^{n}. Linear combinations of vectors. Span of vectors. Linear dependence and independence. Basis. Coordinates. Dimension. 
3.13.4 
3/2 
Kernel and image of a linear transformation. Kernel Image (RankNullity) theorem.  3.3 
3/9 
Midterm I on 3/9;
Kernel Image (RankNullity) theorem.  3.3 
3/16 
Linear transformations and their matrices. Change of a basis.  3.4 
3/22 
Linear spaces. Linear transformations and their matrices. Isomorphisms.  4.14.2 
3/30 
Inner product spaces. Euclidean space R^{n}. Orthogonality. 
5.1 
4/6  Spring break 

4/13 
Orthogonal projections.
Orthogonal complement. CauchySchwarz inequality, Pythagorean Theorem.
GramSchmidt orthogonalization. General inner product spaces.  5.1 5.2, some of 5.5 
4/20 
Midterm II on Apr 20; Determinants. 
6.1 
4/27 
Determinants and their geometrical interpretation. Properties of determinants. 
6.16.3 
5/4 
Eigenvalues and eigenvectors. Eigenspaces. Characteristic equation. Eigenbasis. Diagonalization. 
7.17.4 
Friday 5/15 11:001:30 
Final exam
 
