| 2012-01-17 | lecture:
introduction &
motivation | - course organization
- review of algebra and systems of equations
- high-level overview of the course material
- vectors, planes, spaces, and ways to
symbolically represent them - lecture notes
- related readings [Lay 2003]: 1.1, 1.3
|
| 2012-01-19 | lecture:
vectors | - lecture notes
- algebraic properties of vectors
- vector space axioms
- related readings [Lay 2003]: 1.3
|
| 2012-01-23 | | |
| 2012-01-24 | lecture:
vectors | - lecture notes
- vector norms and dot products in R2
- vector properties and relationships:
- orthogonality
- linear dependence and independence
- projections
- linear combinations
- spans
- related readings [Lay 2003]: 6.1, 6.2, 6.3
|
| 2012-01-26 | lecture:
vectors | - lecture notes
- review of set and predicate notation
- review of vector properties and relationships
- exercises and examples
- related readings [Lay 2003]: 1.3, 1.7
|
| 2012-01-31 | lecture:
matrices | - lecture notes
- linear combinations in applications
- from linear combinations to matrices
- interpretations of matrices
- matrix operations and properties
- related readings [Lay 2003]: 1.6, 2.1
|
| 2012-02-02 | lecture:
matrices | - review: matrix interpretations in applications
- review: maps, composition, and inversion
- composition of matrices and applications
- related readings [Lay 2003]: 2.1, 2.2, 2.3
|
| 2012-02-03 | | |
| 2012-02-04 | | |
| 2012-02-07 | lecture:
matrices | - lecture notes
- review of relations and functions
- matrix multiplication and inversion
- interpretations
- review of algebraic properties
- some subsets of Rn×n and properties
- determinants and inversion of R2×2 matrices
- related readings [Lay 2003]: 2.1, 2.2, 2.3
|
| 2012-02-09 | lecture:
matrices | - lecture notes
- details about subsets of Rn×n and properties
- solving Mv = w for M with various properties
- elementary matrices and row operations
- reduced row echelon forms of matrices
- related readings [Lay 2003]: 1.2, 2.3, 2.5
|
| 2012-02-14 | lecture:
matrices | - lecture notes
- more facts about invertible matrices
- matrix LU factorization
- matrix transposition
- orthogonal matrices
- matrix rank
- matrix similarity
- related readings [Lay 2003]: 1.2, 2.5
|
| 2012-02-16 | lecture:
review | |
| 2012-02-20 | | |
| 2012-02-21 | monday schedule | |
| 2012-02-23 | midterm exam | |
| 2012-02-28 | lecture:
vector spaces | - lecture notes
- sets of vectors and their notation
- computing equality of vector spaces
- abstract vector spaces
- fitting functions to data points
|
| 2012-03-01 | lecture:
vector spaces | - lecture notes
- more on computing equality of spans
- more abstract vector spaces
- fitting functions to many data points
- subspaces
- basis of a vector space
|
| 2012-03-02 | | |
| 2012-03-06 | lecture:
vector spaces | - lecture notes
- computing an orthonormal basis
- projecting onto a subspace
- least-squares approximations
- dimension of a vector space
- orthogonal complement of a vector space
- algebra of vector spaces
|
| 2012-03-08 | lecture:
vector spaces | - lecture notes
- more on fitting functions to data
- approximating a matrix system model
- algebra of vector spaces
- review and more properties of maps
|
| 2012-03-12 | | |
| 2012-03-13 | spring recess | |
| 2012-03-15 | spring recess | |
| 2012-03-20 | lecture:
linear
transformations | - lecture notes
- review and more properties of maps
- homomorphisms and linear transformations
- properties of linear transformations
|
| 2012-03-22 | lecture:
linear
transformations | - lecture notes
- data modelling as a linear transformation
- more properties of linear transformations
- kernel of a linear transformation
|
| 2012-03-27 | lecture:
review | |
| 2012-03-29 | midterm exam | |
| 2012-04-03 | lecture:
linear
transformations | - review of midterm questions
|
| 2012-04-04 | | |
| 2012-04-05 | lecture:
linear
transformations | |
| 2012-04-10 | lecture:
applications to
linear systems | - lecture notes
- linear transformations in applications
- span, dim, ⊥, ker, and im in applications
- examples
- observable systems
- compression and encryption
|
| 2012-04-12 | lecture:
applications to
linear systems | |
| 2012-04-17 | lecture:
applications to
linear systems | |
| 2012-04-19 | lecture:
applications to
linear systems | |
| 2012-04-24 | lecture:
eigenvectors &
eigenvalues | |
| 2012-04-26 | lecture:
review | |
| 2012-04-29 | | |
| 2012-05-01 | lecture:
review | |
2012-05-09
Wed. 3-5 PM | final exam | |