Math 230 (Spring 2011): Topics covered, and Lecture notes in Honors Introductory Linear Algerbra
Note to students: The scribes posted here are exactly what I write in class during the lecture. At the same time, they may not contain everything I say during the lecture! So, there are still plenty of reasons to come to class. |
Lec # | Date | Topic(s) | Notes |
---|---|---|---|
1 | Jan 11 | syllabus, 2D example, graphical solution, elementary row operations (EROs), augmented matrix | Lec 1 scribe |
2 | Jan 13 | inconsistent system, using EROs to solve a system of linear equations, echelon and reduced echelon form of matrices | Lec 2 scribe |
3 | Jan 18 | pivots, row reduction, basic and free variables, general solution of a system of linear equations, vector equations | Lec 3 scribe |
4 | Jan 20 | linear combination of vectors, span, plane through origin, properties of R^{n}, intro to MATLAB on my.math.wsu.edu | Lec 4 scribe |
5 | Jan 25 | matrix equation Ax=b, matrix-vector multiplication and properties, pivot in every row to span R^{m} | Lec 5 scribe |
6 | Jan 27 | correct notation for replacement EROs, homogeneous system, trivial and nontrivial solutions, parametric vector form | Lec 6 scribe |
7 | Feb 1 | Row and column pictures of Ax=0 and Ax=b, application - market equilibrium, MATLAB session | Lec 7 scribe |
8 | Feb 3 | market equilibrium - more MATLAB, linearly (in)dependent (LD/LI) vectors, | Lec 8 scribe |
9 | Feb 8 | special case of LI/LD vectors, characterization of all LD sets of vectors, linear transformations (LT) | Lec 9 scribe |
10 | Feb 10 | domain, codomain, and range of a transformation, definition of an LT, example of a non-linear transformation | Lec 10 scribe |
11 | Feb 15 | matrix of an LT, geometric LTs in 2D (rotation, reflection, shear), projection from R^{n} to R^{2} | Lec 11 scribe |
12 | Feb 17 | onto and one-to-one mappings, onto and 1-to-1 LTs, pivots in every row/column, Applications - population migration | Lec 12 scribe |
13 | Feb 22 | properties of matrix addition, scalar multiplication, (properties of) matrix multiplication, transpose of a matrix | Lec 13 scribe |
14 | Feb 24 | inverse of a matrix, determinant of a 2 x 2 matrix, review for midterm | Lec 14 scribe |
15 | Mar 1 | midterm exam | Midterm |
16 | Mar 3 | inverse of a matrix, properties of matrix inverses, inverse of an n x n matrix, algorithm to find matrix inverse | Lec 16 scribe |
17 | Mar 8 | properties of invertible matrix, inverses of structured matrices, invertible matrix theorem (IMT) | Lec 17 scribe |
18 | Mar 10 | IMT, inverse transformation, determinants, expanding along any row or column, replacement ERO and determinant | Lec 18 scribe |
19 | Mar 22 | EROs and determinants, combining EROs and cofactor expansion, properties of determinants, proof by induction | Lec 19 scribe |
20 | Mar 24 | iterations in MATLAB, creating and using functions in MATLAB | Lec 20 scribe |
21 | Mar 29 | functions in MATLAB - DoSomething.m, definition of vector spaces, set of all polynomial with degree up to n | Lec 21 scribe |
22 | Mar 31 | uniqueness of zero of a vector space, subspaces, span of a set of elements of a vector space is a subspace | Lec 22 scribe |
23 | Apr 5 | intersection of subspaces, nullspace and column space of A (Nul A and Col A), description of Nul A | Lec 23 scribe |
24 | Apr 7 | comparing Nul A and Col A, LI sets, basis of a subspace, bases for Nul A and Col A, dimension of a subspace | Lec 24 scribe |
25 | Apr 12 | discussion of computer project, illustration of the algorithm on a 3 x 4 matrix | Lec 25 scribe |
26 | Apr 14 | dimension of vector space, basis theorem, basis for P_{3}, rank of A, rank theorem, IMT continued | Lec 26 scribe |
27 | Apr 19 | eigenvalues and eigenvectors, symmetric A has real eigenvalues, triangular matrices, characteristic polynomial | Lec 27 scribe |
28 | Apr 21 | eigenspace, multiplicity of eigenvalue, similar matrices have same set of eigenvalues, QR algorithm | Lec 28 scribe |
29 | Apr 26 | demo of QR algorithm, volume of parallelepiped from determinant, replacement EROs and eigenvalues | Lec 29 scribe |
30 | Apr 28 | eigenvectors of distinct eigenvalues are LI, review for final exam | Lec 30 scribe |