| Week |
Topic |
| 1 |
1 Matrices, Operations on Matrices, Partitioned Matrices, Matrix Form of A Linear system, Row Echelon and Reduced Row Echelon Forms, Gauss Elimination and Gauss Jordan Elimination, Matrices Defining Transformations |
| 2 |
2 Matrix Arithmetic, Zero and Identity Matrices, Inverse Matrices, Properties of Powers and Transposes, Elementary Matrix and Row Operations, Systems of Equations and Invertibility |
| 3 |
3 Simultaneous Solutions of Multiple Systems, Special Matrices (Diagonal, Triangular, Symmetric), Determinants, Inverse of A Matrix by Adjoint Computation, Determinants of Triangular Matrices |
| 4 |
4 Cramer's rule, Properties of the Determinant, Technique for Determinant Evaluation based on Elementary Row Operations, Determinants of Inverse Matrices |
| 5 |
5 Vectors, Arithmetic, Dot Product, Norm, Orthogonal Vectors, Orthogonal Projection, Distance between a Point and a Line, Cross Prouduct, Vector Representation of Lines and Planes, Intersection of Two Planes |
| 6 |
6 Euclidean Vector Spaces, Cauchy-Schwartz and Triangle Inequalities, Linear Transformations, Standard Matrices, Reflection, Projection, Rotation, Dilation, Contraction, composition of Linear Transformations, Properties of Linear Transformations, Inverse Transformations, |
| 7 |
8 Linearity, Standard Basis Vectors, Standard Matrix in terms of Images of Standard Basis Vectors, Affine Transformations, Vector Spaces, Subspace, Examples of Vector Spaces and Subspaces,Homogeneous Linear Systems as Subspaces, Linear Combination- Span- Subspace |
| 8 |
Midterm (120 minutes- topics until Vector Spaces) |
| 9 |
9 Linear Independence, Geometric Consequences of Linear Independence, Functional Spaces and Linearly Independent Functions, Wronskian, Basis and Dimension, The Coordinates Relative to a Basis |
| 10 |
10 Finite and Infinite Dimensional Vector Spaces, Dimension- Span and Linear Independence, +/- Theorem, Further Theorems, Solution Spaces of Linear & Homogeneous Systems, Rowspace, Columnspace, Nullspace |
| 11 |
11 Homogeneous, Particular and General Solutions, Determining Bases of Rowspace and Columnspace, Rank, Nullity,Consistency- Solution Space and Rank, Overdetermined and Underdetermined Systems |
| 12 |
12 Inner Product Spaces, Gram Schmidt Orthonormalization, QR Decomposition, Orthonormal Bases, Least Squares |
| 13 |
13 Change of Basis, Eigenvalues and Eigenvectors, Diagonalization |
| 14 |
Orthogonal Diagonalization, Recitation (time permitting) |