### Linear Algebra Math 2270-002 Fall 2018 Lecture Page

Department of Mathematics
College of Science
University of Utah

Lecture notes for each week by late Friday afternoon of preceding week. I will bring printed versions of each week's packets to class on Mondays. It is recommended that you use these notes in conjunction with attending class. After each class I will post the filled-in versions for that day. At the end of the week I'll post the entire week's filled-in notes.

Week 1: August 20-24 Sections 1.1-1.3
week1.pdf Notes that include outline for entire week
aug20.pdf   syllabus discussion; introduction to 1.1, systems of linear equations.
aug21.pdf   1.1-1.2 introduction to Gaussian elimination
aug22.pdf   1.2 Gaussian elimination and reduced row echelon form
aug24.pdf   1.2-1.3 review of reduced row echelon form; recalling vector addition and scalar multiplication, algebraically and geometrically.
week1_post.pdf   filled-in class notes for week 1.

Week 2: August 27-September 1 Sections 1.3-1.6
week2.pdf Notes that include outline for entire week
aug27.pdf   1.3 linear combinations and vector equations
aug28.pdf   1.3-1.4 vector equations and linear systems of equations are matrix equations.
aug29.pdf   1.4-1.5 solution sets for matrix equations, based on rref considerations.
aug31.pdf   1.5-1.6 solution sets for matrix equations, based on rref considerations; applications.
week2_post.pdf   filled-in class notes for week 2.

Week 3: September 4-7 Sections 1.6-1.8
week3.pdf Notes that include outline for entire week
sept4.pdf   1.6-1.7 applications; introduction to linear dependence/independence
sept5.pdf   1.7 linear independence/dependence answers via reduced row echelon form
sept7.pdf   1.7-1.8 column dependencies, homogeneous solutions, and reduced row echelon form; brief intro to linear transformations.
week3_post.pdf   filled-in class notes for week 3.

Week 4: September 10-14 Sections 1.8-2.2
week4.pdf Notes that include outline for entire week
sept10.pdf   1.8-1.9 linear (matrix) transformations from Rn to Rm
sept11.pdf   1.8-1.9 continued, emphasis on transformations of the plane to itself.
sept12.pdf   1.8-1.9 review, "one-one" and "onto" functions interpreted for matrix transformations.
sept14.pdf   2.1-2.2 introduction to matrix algebra and matrix inverses
week4_post.pdf   filled-in class notes for week 4.

Week 5: September 17-21 Sections 2.1-2.3, 3.1
week5.pdf Notes that include outline for entire week
sept17.pdf   2.1-2.2 matrix algebra and inverses, continued
sept18.pdf   2.2 matrix inverses (2.3 is mostly a concepts integration section)
sept19.pdf   2.2 matrix inverses re-interpreted using elementary matrices.
sept21.pdf   3.1, intro to 3.3 determinants and magic inverse formulas. Also discussion of "affine transformation" homework.
week5_post.pdf   filled-in class notes for week 5.

Week 6: September 24-26 Sections 3.2-3.3, with tie in to 1.9 and exam review.
week6.pdf Notes that include outline for entire week
sept24.pdf   3.2, properties of determinants, in relation to elementary row operations
sept25.pdf   3.2-3.3, why determinant is an invertiblity check; adjugate formula for matrix inverses, and Cramer's rule.
sept26.pdf   3.3 how determinants track area/volume expansion factors (and reflections) in all dimensions, and some concepts review for exam.
week6_post.pdf   filled-in class notes for week 6.

Week 7: October 1-5 Sections 4.1-4.3
week7.pdf Notes that include outline for entire week
oct1.pdf   4.1 introduction to vector spaces and sub vector spaces
oct2.pdf   4.1-4.2 introduction to vector spaces and sub vector spaces, examples from Rn and function vector spaces.
oct3.pdf   4.2 subspace examples, Nul A.
oct5.pdf   4.2-4.3 Nul A, Col A, ker T, range T, bases for subspaces.
week7_post.pdf   filled-in class notes for week 7.

Week 8: October 15-19 Sections 4.2-4.6
week8.pdf Notes that include outline for entire week
oct15.pdf   4.1-4.3 review and completed
oct16.pdf   4.4 each basis for a vector space yields a coordinate system for that vector space.
oct17.pdf   4.4 completed
oct19.pdf   4.5-4.6 vector space theorems; the four fundamental subspaces associated to a matrix.
week8_post.pdf   filled-in class notes for week 8.

Week 9: October 22-26 Sections 4.5-4.6, 4.9, 5.1-5.2
week9.pdf Notes that include outline for entire week
oct22.pdf   4.5 vector space theorems completed
oct24.pdf   4.6 rank and nullity, and the four fundamental subspaces associated to a matrix, completed.
oct26.pdf   4.9 Stochastic matrices, Markov chains, google page rank.
week9_post.pdf   filled-in class notes for week 9.

Week 10: October 29 - Nov 2 Sections 4.9, 5.1-5.4
week10.pdf Notes that include outline for entire week
oct29.pdf   4.9-5.2: google page rank as steady state vector for voting game; introduction to more general eigenvectors and eigenvalues.
oct30.pdf   5.2: finding eigenvalues and eigenspace bases for square matrices.
oct31.pdf   5.3: matrix diagonalization
nov2.pdf   5.4: eigenvalues, eigenvectors and matrices for linear transformations
week10_post.pdf   filled-in class notes for week 10.

Week 11: Nov 5-7 Sections 5.4-5.5, 6.1
week11.pdf Notes that include outline for entire week
nov5.pdf   5.4 change of basis for linear transformations, continued.
nov6.pdf   5.5 complex eigendata
nov7.pdf   Appendix B - the complex plane. These are replacement notes for Wednesday.
week11_post.pdf   filled-in class notes for week 11.

Week 12: Nov 12-16 Sections 6.1-6.4
week12.pdf Notes that include outline for entire week
nov12.pdf  6.1 algebra and geometry of dot product; orthogonal projection onto lines (from 6.2).
nov13.pdf  6.1-6.2 angles in Rn, orthogonal complements and matrix subspaces.
nov14.pdf  6.2 orthogonal complements
nov16.pdf  6.2-6.4 orthogonal projections onto higher-dimensional subspaces; Gram-Schmidt algorithm intro.
week12_post.pdf   filled-in class notes for week 12.

Week 13: Nov 19-21 Sections 6.4-6.6
week13.pdf Notes that include outline for entire week
nov19.pdf   6.4 Gram-Schmidt algorithm, and A = Q R matrix factorizations.
nov20.pdf   6.4 orthogonal matrices; 6.5 least squares solutions
nov21.pdf   6.5-6.6 least squares solutions and applications to linear modeling
week13_post.pdf   filled-in class notes for week 13.

Week 14: Nov 26-30 Sections 6.6-6.8, 7.1-7.2
week14.pdf Notes that include outline for entire week
nov26.pdf   6.6-6.7 Power laws and linear regression for log-log data; introduction to inner product spaces.
nov27.pdf   6.7-6.8 inner product space example; Fourier series
nov28.pdf   6.8 Fourier series and image compression show and tell
nov30.pdf   7.1-7.2 Spectral theorem and diagonalizing quadratic forms
week14_post.pdf   filled-in class notes for week 14.

Week 15: Dec 3-5 Sections 7.1-7.2, supplementary material on principal component analysis
week15.pdf (Wednesday notes not yet added).
dec3.pdf   7.1-7.2, diagonalization example; spectral decomposition for symmetric matrices and other preliminaries for Prof. Alberts' guest lecture on Tuesday.
dec4: PCA_and_DNA___Undergrad_Colloquium Prof. Alberts' slides from his presentation.
dec5.pdf   course review notes