Honors Introductory Linear ALgebra -- Lecture Notes

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.

Scribes from all lectures (as a single big file)

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 Rn, 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 Rm 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 Rn to R2 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 P3, 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

Scribes from all lectures (as a single big file)