Estimated schedule for Math 369 (section 1): Linear Algebra

Please note that this is JUST an estimate (and was stolen from Prof. Jeff Achter, another instructor of 369 this semester).

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Week Topic Ref
1 Systems of linear equations
examples and applications; row reduction; echelon forms;
associated(augmented) matrices
WILA What is Linear Algebra?
SSLE Solving Systems of Linear Equations
RREF Reduced Row-Echelon Form
2 Matrix equations
Rn; arithmetic of vectors; Ax=b
structure of (in)homogeneous solutions
VO Vector Operations
MO Matrix Operations
MM Matrix Multiplication
3 Matrix operations
matrix multiplication; row operations;
inverse matrices; span.
MM Matrix Multiplication
MISLE Matrix Inverses and Systems of Linear Equations
LC Linear Combinations
SS Spanning Sets
4 Independence
linear independence;
column space; solvability; rank
LI Linear Independence
LDS Linear Dependence and Spans
CRS Column and Row Spaces
5 Factorizations, determinants DM Determinant of a Matrix
PDM Properties of Determinants of Matrices
6 Backwards and forwards
review; exam;
abstract vector spaces
VS Vector Spaces
7 Vector spaces
dimension; basis; coordinates
S Subspaces
LISS Linear Independence and Spanning Sets
B Bases
D Dimension
PD Properties of Dimension
8 Transformations
linear transformations; change of coordinates
LT Linear Transformations
VR Vector Representations
MR Matrix Representations
CB Change of Basis
9 Eigenvectors
eigenvalues and eigenvectors; geometry;
EE Eigenvalues and Eigenvectors
PEE Properties of Eigenvalues and Eigenvectors
10 Eigenvectors II
characteristic polynomial; diagonalization; applications
11 Applications
markov chains; graph theory; numerics
12 Backwards and forwards
review; exam; inner products
13 Inner products
orthogonality; projection; Gram-Schmidt
Section O Orthogonality
14 Decompositions
least squares; QR; SVD
15 Wrapping up
applications; review