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Math 113 - Linear Algebra and Matrix Theory
Stanford Mathematics, Summer 2017
Instructor: Christopher Ohrt, 382-Q1, [email protected]: Ben Dozier, [email protected] meets: MTWTh 12:30pm-1:20pm, 200-203Office Hours: Instructor: Tu 1:30pm-2:30pm, Th 2:30pm-3:30pm; TA:Prerequisites: No formal prerequisites, though familiarity with basic linear algebra will be veryhelpfulTextbook: Sheldon Axler, Linear Algebra Done Right, 3rd edition (2015)
Course Material: Algebraic properties of matrices and their interpretation in geometric terms.The relationship between the algebraic and geometric points of view and matters fundamental to thestudy and solution of linear equations. Topics: linear equations, vector spaces, linear dependence,bases and coordinate systems; linear transformations and matrices; similarity; eigenvectors andeigenvalues; diagonalization.
Grading: The final grade is based on the following grading scheme:
20% Homework + 30% Midterm + 50% Final
Homework is assigned weekly and collected at the beginning of the class on Monday. Thereis no make-up homework. However, the lowest homework score is dropped from the computation ofyour grade.
The midterm takes place on Monday of week 5, July 24th during the regular class hours.There are no make-up midterms. If you miss a midterm for a good reason, the weight from thismidterm will be carried by the final exam. You should contact the instructor as soon as possible ifyou anticipate this happening.
The final exam will take place on Saturday, August 19th from 12:15-3:15pm in 200-203. Thedate and time of the final exam cannot be changed. You must attend the final exam in order to passthe class.
Grading questions: If you have a grading question about one of the assignments, it should bebrought to the attention of the instructor within 14 calendar days of the due date of the exam.
Schedule: We will try keep to the following schedule:
Week Date Section Topics1 6/26 1.A Introduction, Rn and Cn
6/27 1.B Definition of a Vector Space6/28 1.C Subspaces and Sums6/29 2.A Spans and Linear Combinations
2 7/03 2.A/B Linear Independence and Basis7/04 Independence Day7/05 2.B/C Basis and Dimension7/06 3.A/B Maps and Linear Maps
3 7/10 3.A Rank and Nullity7/11 3.C Matrices and Matrix Representation7/12 3.C Matrix Representation and Matrix Multiplication7/13 3.D Invertibility and Isomorphisms
4 7/17 3.E Products and Quotients7/18 3.F Dual Spaces7/19 4/5.B Polynomials (applied to Operators)7/20 5.A Eigenvalues and Eigenvectors
5 7/24 Midterm7/25 5.B Existence of Eigenvalues7/26 5.B/C Upper Triangular and Diagonal Matrices7/27 6.A Inner Products and Norms
6 7/31 6.B ONB’s and Gram Schmidt8/01 6.B/C Gram Schmidt and Applications8/02 7.A Adjoints and Self-Adjoint/Normal Operators8/03 7.A/B Eigenvalues of Self-Adjoint Operators
7 8/07 7.B Spectral Theorem over R and C8/08 8.A Generalized Eigenvectors8/09 8.B Multiplicity and Block-form8/10 8.C Characteristic Polynomial
8 8/14 8.C/D Minimal Polynomial and Jordan Normal Form8/15 10.A Trace8/16 10.B Determinant8/17 Review
