Math 230: Lecture Notes and Videos on Honors Introductory Linear Algebra
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Copyright: I (Bala Krishnamoorthy) hold the copyright
for all lecture scribes/notes, documents, and other
materials including videos posted on these course web
pages. These materials might not be used for commercial
purposes without my consent.
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Scribes from
all lectures so far (as a single big file)
| Lec | Date | Topic(s) | Scribe |
| 1 |
Jan 11 |
syllabus, 2D example, graphical solution, elementary row
operations (EROs), augmented matrix
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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
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| 3 | Jan 18 |
pivots, row reduction, basic and free variables, general solution of a
system of linear equations, vector equations
| Lec 3 scribe
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| 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
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| 5 | Jan 25 |
matrix equation Ax=b, matrix-vector
multiplication and properties, pivot in every row to span
Rm
| Lec 5 scribe
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| 6 | Jan 27 |
correct notation for replacement EROs, homogeneous system, trivial and nontrivial solutions,
parametric vector form
| Lec 6 scribe
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| 7 | Feb 1 |
Row and column pictures of Ax=0 and
Ax=b, application - market
equilibrium, MATLAB
session
| Lec 7 scribe
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| 8 | Feb 3 |
market equilibrium
- more
MATLAB, linearly (in)dependent (LD/LI) vectors,
| Lec 8 scribe
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| 9 | Feb 8 |
special case of LI/LD vectors, characterization of all LD sets of
vectors, linear transformations (LT)
| Lec 9 scribe
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| 10 | Feb 10 |
domain, codomain, and range of a transformation, definition of an LT,
example of a non-linear transformation
| Lec 10 scribe
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| 11 | Feb 15 |
matrix of an LT, geometric LTs in 2D (rotation, reflection, shear),
projection from Rn to
R2
| Lec 11 scribe
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| 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
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| 13 | Feb 22 |
properties of matrix addition, scalar multiplication, (properties of)
matrix multiplication, transpose of a matrix
| Lec 13 scribe
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| 14 | Feb 24 |
inverse of a matrix, determinant of a 2 x 2 matrix, review for
midterm
| Lec 14 scribe
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| 15 | Mar 1 |
midterm exam | Midterm
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| 16 | Mar 3 |
inverse of a matrix, properties of matrix inverses,
inverse of an n x n matrix, algorithm to
find matrix inverse
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Lec 16 scribe
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| 17 | Mar 8 |
properties of invertible matrix, inverses of structured
matrices, invertible matrix theorem (IMT)
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Lec 17 scribe
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| 18 | Mar 10 |
IMT, inverse transformation, determinants, expanding along
any row or column, replacement ERO and determinant |
Lec 18 scribe
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| 19 | Mar 22 |
EROs and determinants, combining EROs and cofactor
expansion, properties of determinants, proof by induction |
Lec 19 scribe
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| 20 | Mar 24 |
iterations
in MATLAB, creating and using functions in MATLAB
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Lec 20 scribe
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| 21 | Mar 29 |
functions in MATLAB
- DoSomething.m,
definition of vector spaces, set of all polynomial with
degree up to n
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Lec 21 scribe
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| 22 | Mar 31 |
uniqueness of zero of a vector space, subspaces, span of a set of
elements of a vector space is a subspace
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Lec 22 scribe
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| 23 | Apr 5 |
intersection of subspaces, nullspace and column space
of A (Nul A and Col A), description of
Nul A
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Lec 23 scribe
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| 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
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Lec 24 scribe
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| 25 | Apr 12 |
discussion
of computer
project, illustration
of the algorithm on a 3 x 4 matrix
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Lec 25 scribe
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| 26 | Apr 14 |
dimension of vector space, basis theorem, basis
for P3, rank of
A, rank theorem, IMT continued
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Lec 26 scribe
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| 27 | Apr 19 |
eigenvalues and eigenvectors, symmetric A has
real eigenvalues, triangular matrices, characteristic
polynomial
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Lec 27 scribe
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| 28 | Apr 21 |
eigenspace, multiplicity of eigenvalue, similar matrices
have same set of eigenvalues, QR algorithm
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Lec 28 scribe
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| 29 | Apr 26 |
demo of QR algorithm, volume of parallelepiped from
determinant, replacement EROs and eigenvalues
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Lec 29 scribe
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| 30 | Apr 28 |
eigenvectors of distinct eigenvalues are LI, review
for final exam
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Lec 30 scribe
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Last modified: Thu May 5 12:27:12 PDT 2011
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