20130117  lecture: introduction & motivation   course organization
 lecture notes
 highlevel overview of course material
 models, systems, and system states
 review of algebra of real numbers
 vectors and vector addition
 related readings:

20130122  lecture: vectors   lecture notes
 more about algebraic properties
 more review of logical formulas
 vector addition & scalar multiplication
 vector norms and dot products in R^{2}
 linear dependence and independence
 orthogonality of vectors
 related readings:
 [Lay 2012]: 6.1; 6.2
 [Bretscher 2009]: 1.3.6; 5.1; A.4

20130124  lecture: vectors   lecture notes
 properties of equality
 more proof examples and strategies
 projections of vectors onto vectors
 vector negation and subtraction
 related readings:
 [Lay 2012]: 6.1; 6.2
 [Bretscher 2009]: 2.2; 5.1; 5.5.2

20130129  lecture: vectors   lecture notes
 review of orthogonal projections
 lines (as sets of vectors)
 vector equations and y = mx + b
 linear combinations of vectors
 related readings:
 [Lay 2012]: 6.1
 [Bretscher 2009]: 2.2

20130131  lecture: vectors   lecture notes
 lines and planes (as sets of vectors)
 more practice with vector properties
 linear combinations in applications
 related readings:
 [Lay 2012]: 1.10; 6.1
 [Bretscher 2009]: 2.2

20130204   
20130205  lecture: matrices   lecture notes
 linear combinations in applications
 from linear combinations to matrices
 interpretations of matrices
 matrix operations and properties
 related readings:
 [Lay 2012]: 1.6; 1.10; 2.1

20130207  lecture: matrices   lecture notes
 review: maps and composition
 matrix multiplication
 derived dimension relationships
 system states over time
 some subsets of R^{n×n} and properties
 identity matrix
 scalar matrices
 diaigonal matrices
 related readings:
 [Lay 2012]: 1.10; 2.1
 [Bretscher 2009]: 2.1; 2.3

20130212  lecture: matrices   lecture notes
 invertible matrices
 determinant & inverse of R^{2×2} matrix
 related readings:
 [Lay 2012]: 2.1; 2.2; 2.3
 [Bretscher 2009]: 2.1; 2.3; 2.4

20130214  lecture: matrices   lecture notes
 more subsets of R^{n×n} and properties
 upper triangular matrices
 lower triangular matrices
 Mv = w for M with various properties
 elementary matrices & row operations
 reduced row echelon forms of matrices
 related readings:
 [Lay 2012]: 1.2; 2.3; 2.5
 [Bretscher 2009]: 1.2; 1.3; 2.4

20130215   
20130219  lecture: matrices   lecture notes
 elementary matrices & row operations
 more facts about invertible matrices
 matrix PLU factorization
 related readings:
 [Lay 2012]: 1.2; 2.3; 2.5
 [Bretscher 2009]: 1.2; 1.3; 2.4

20130221  lecture: matrices   lecture notes
 more on rref & row operations
 basic example from physics
 orthogonal matrices and rotations
 related readings:
 [Lay 2012]: 1.2; 2.3; 2.5
 [Bretscher 2009]: 1.2; 1.3; 2.4

20130226  lecture: matrices & vector spaces   lecture notes
 orthogonal matrices and rotations
 matrix rank
 introduction to vector spaces
 sets of vectors and their notation

20130228  lecture: review  
20130301   
20130305 Tuesday 3:305 PM  midterm exam  
20130307  lecture: vector spaces   review of midterm problems
 lecture notes
 spans of vectors
 equality of spans

20130312  spring recess  
20130314  spring recess  
20130319  lecture: vector spaces   lecture notes
 sets of vectors
 span notation for sets of vectors
 membership in spans
 equality of spans
 related readings:
 [Lay 2012]: 4.1; 4.3
 [Bretscher 2009]: 3.1.2; 3.2; 4.1

20130321  lecture: vector spaces   lecture notes
 abstract vector spaces
 sets of polynomials as vector spaces
 fitting polynomials to points in R^{2}
 related readings:

20130326  lecture: vector spaces   lecture notes
 sets of polynomials as vector spaces
 fitting polynomials to points in R^{2}
 basis and dimension of a vector space
 related readings:
 [Lay 2012]: 4.3; 4.5
 [Bretscher 2009]: 3.2; 3.3; 4.1

20130328  lecture: vector spaces   lecture notes
 basis and dimension of a vector space
 orthonormal basis of a vector space
 GramSchmidt process
 related readings:
 [Lay 2012]: 4.3; 4.5; 6.2; 6.4
 [Bretscher 2009]: 3.2; 3.3; 5.1; 5.2

20130402  lecture: vector spaces   lecture notes
 projection onto a vector subspace
 over & underdetermined systems
 homogenous & nonhomogenous systems
 leastsquares approximations
 related readings:
 [Lay 2012]: 1.5; 6.2; 6.3
 [Bretscher 2009]: 3.1.2; 3.2; 4.1

20130404  lecture: vector spaces   lecture notes
 leastsquares curve fitting
 applications of curve fitting
 approximating system relationships
 related readings:
 [Lay 2012]: 6.5; 6.6; 8.1
 [Bretscher 2009]: 5.4

20130409  lecture: linear transformations   lecture notes
 distributed computation of leastsquares
 intersections & products of vector spaces
 product spaces, relations, & maps

20130411  lecture: linear transformations   lecture notes
 linear transformations & examples
 injections & surjections
 bijections & isomorphisms
 related readings:
 [Lay 2012]: 1.9; 2.9.1; 4.4.5
 [Bretscher 2009]: 3.1; 3.2; 4.2

20130412   
20130416  lecture: linear transformations   lecture notes
 projection as a linear transformation
 bijections & isomorphisms
 matrices as linear transformations
 related readings:
 [Lay 2012]: 1.9; 2.9.1; 4.4.5
 [Bretscher 2009]: 3.1; 3.2; 4.2; 5.4

20130418  monday schedule  
20130423  lecture: applications to linear systems   lecture notes
 affine spaces
 applications in communications
 related readings:

20130425  lecture: eigenvectors & eigenvalues   lecture notes
 fixed points and spaces
 eigenvectors and eigenvalues
 related readings:
 [Lay 2012]: 5.1; 5.2; 5.4
 [Bretscher 2009]: 7.1; 7.2; 7.3

20130430  lecture: review  
20130502  lecture: review  
20130503   
20130509 Thursday 35 PM MCS B23  final exam  