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 R^{n} to R^{m}
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 R^{n} 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 R^{n}, 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 |