Math 223, Section 201

Syllabus

Textbook: K. Jänich. Linear Algebra.

This is the syllabus which lists all topics covered in this course,
and for which you are responsible on the final exam.

The plan is to cover all material from the textbook. Adjusments
will be made during the course, they will be listed here.

Each chapter should take up one week of classes and
one homework assignment.
Here is some additional material you may find useful.

A summary of dynamical systems.
This covers both the discrete and the continuous case (the latter is not on the syllabus).
It's a bit verbose, as it was written for 221.
0.   The Row Reduction Algorithm.
(Augmented) coefficient matrix of a linear system of equations,
Matrices in row echelon form (REF) and reduced row echelon form (RREF), pivots, pivot columns, and pivot variables,
The row reduction algorithm (Gaussian elimination, Gauss-Jordan elimination): forward elimination and back substitution,
General solution of a system of equations in parametric vector form, free variables,
Criterion for solvability.
(All this material is on wikipedia.)
I.   Sets and Maps.
1.1, 1.2, 1.3.
II.   Vector Spaces.
2.1, 2.2, 2.3, 2.4, 2.5, 2.6.
III.   Dimension.
3.1, 3.2, 3.3, 3.4.
IV.   Linear Maps.
4.1, 4.2, 4.3, 4.5.
V.   Matrix Calculus.
5.1, 5.2, 5.3, 5.4, 5.5, 5.6.
VI.   Determinants.
6.1, 6.2, 6.3, formula at top of page 112, 6.5, 6.6, 6.7.
VII.   Systems of Linear Equations.
7.1, 7.3, 7.4, 7.5 (but no column interchages!)
VIII.   Euclidean Vector Spaces.
8.1, 8.2, 8.3 plus uniqueness of Gram-Schmidt and QR-factorization, 8.4, 8.5.
IX.   Eigenvalues.
9.1, 9.2, 9.3, plus discrete dynamical systems
(Chapter 1 of the notes on dynamical systems linked above),
9.4, powers of matrices
X.   The Principal Axes Transformation.
10.1, 10.2, 10.3, 10.4.
XI.   Classification of Matrices.
11.1 (Defn of equivalence relation and equivalence class, p 171 and 172, Remark on p 172), 11.2, 11.3, 11.4, 11.5, 11.6.
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