## Math 321, Linear Algebra, Fall 2008

##### Professor Terry Loring, Department of Mathematics and Statistics,

• I'll send eMail via your UNM accounts. Check this several times per week, or turn on forwarding to an account you frequent: How To #504 - Forward Your UNM Electronic Mail.
• The text is Linear Algebra: A Modern Introduction by David Poole, ISBN 0534341748.
• This text is going to be expensive, so I am going to allow you to use the first edition or the second, and you don't need the CD-ROM.
• This text covers vector spaces over finite numbers systems, not just real and complex, interesting applications, good methods of calculations and the real theory behind it all. Plus it gets rave reviews at Amazon.

#### Week Two, September 1-5, 2008

• Monday: Labor day, no class.
• Wednesday: Dot product. § 1.2
• Homework 2 due in class September 10.
• Friday: A proof of the Cauchy Schwarz Inequality. Projection of one vector on another. § 1.3.

#### Week Three, September 8-12, 2008

• Monday: Lines and Planes: vector form / parametric form of equations. Intro to Systems of Linear Equations. Equivalent Systems. § 2.1
• Wednesday: Solving sytems of linear equations using matrices and row operations. § 2.2.
• Homework 3 due in class September 17.
• Friday: (reduced) row echelon form. How to pick the free variables. Gauss Elimination. Systems with scalars in Z-mod-2.

#### Week Four, September 15-19, 2008

• Monday: Rank. Linear Independence in R^n. § 2.3.
• Wednesday: Span of a set of vectors.
• Homework 4 due in class September 26.
• We are skipping § 2.4 and § 2.5. However, you might find § 2.4 helpful on the homework.
• Friday: Matrix Multiplication. § 3.1.

#### Week Five, September 22-26, 2008

• Monday: Matrix algebra. § 3.2.
• Wednesday: Inverse of a Matrix. Elementary Matrices. § 3.3
• Friday: Computing inverses.
• Before Monday work on this Review I

#### Week Six, September 29 - October 3, 2008

• Monday: Review.
• Overall grading will be: HW 20%; MidI 25%; MidII 25%; Final 30%.
• Wednesday: Midterm I (October 1).
• Friday: Gauss-Jordan to invert matrices.

#### Week Eight, October 13-17, 2008

• Monday: dimension, nullity, rank
• Homework 6 due in class October 22.
• Wednesday: Linear transformations between standard vector spaces. § 3.6
• Th, F: October 16-17, Fall break, no classes.

#### Week Ten, October 27-31, 2008

• Monday: Determinants and Row operations, continued.
• Wednesday: lecture cancelled.
• Computing determinants several ways.
• Friday: Determinants of products and transposes. § 4.2.
• We are skipping Cramer's rule.

#### Week Eleven, November 3-7, 2008

• Monday: Eigenvalues via the characteristic polynomial. § 4.3.
• Homework 8 due in class November 10.
• Wednesday: Similarity and diagonalization. § 4.4.
• Friday: Diagonalization, continued.
• Before Monday work on these Review II
• Also look over the last four homeworks!

#### Week Twelve, November 10-14, 2008

• Monday: Review
• Wednesday: Midterm II (November 12).
• Friday: power methods to find eigenvalues and eigenvectors § 4.5.

#### Week Thirteen, November 17-21, 2008

• Monday: Stochasitc matrices, § 4.6.
• Wednesday: Orthogonal matrices, orthonormal sets of vectors § 5.1.
• Homework 9 due in class November 26.
• Friday: orthogonal projection § 5.2.

#### Week Fourteen, November 24-28, 2008

• Monday: Gram-Schmidt process. § 5.3.
• Wednesday: Orthogonal diagonalizatino § 5.4.
• Th, F: Thanksgiving break, no classes, November 27-28,

#### Week Fifteen, December 1-5, 2008

• Homework 10 due in class December 5.
• Monday: § 6.1-2 Abstract and infinite dimensional vector spaces. Basis.
• Wednesday: § 6.4. Linear transformation. § 6.6. Matrix of a linear transformation
• Friday: Isomorphism.

#### Week Sixteen, December 8-12, 2008

• To keep you busy: Review III
• Monday: Questions from homework assignments.
• Wednesday: Review
• Friday: Review

#### Finals Week

• Thursday: office hours 1-3
• Fall 2008 exam schedule
• Friday: Final. December 19, 2008, 3:00-5:00 p.m. (the time for all MWF 3:00-3:50 classes).