MAT 2141 (Fall 2010)

Linear Algebra I

Syllabus

The syllabus will be updated as the course progresses. Unless otherwise indicated, section numbers and exercises refer to the text Linear Algebra by Sterling K. Berberian.

Date Text Sections Material Recommended Exercises*
Sep 9 Lecture notes only Sets with operations (magmas) Exercises in notes only
Sep 13 A.4 Fields Exercises in notes only
Sep 16 1.3 Vector spaces: definition and examples Page 14: Exercises 1, 3, 4
Sep 20 1.3–1.6 Some properties of vector spaces, linear combinations, subspaces Page 17: Exercises 1–5; Page 19: Exercises: 1, 4–8
Sep 23 1.6 Subspaces Page 22: Exercises (3)–(5), (8), (10), (11), (13), (16), (17)
Sep 27 2.1, 2.2 Linear mappings Page 28: Exercises (1)–(4), (7); Page 31: Exercise (3)
Sep 30 2.2, 2.3 Kernel, image, vector spaces of linear mappings Page 31: Exercises (1), (2), (4)–(6); Page 35: Exercises (2), (3), (11)–(16), (19), (20)
Oct 4 2.3, 2.4 Isomorphisms Page 35: Exercises (9), (10), (21), (23), (24); Page 39: Exercises (2), (5)–(11),
Oct 7 2.4, 2.5 Isomorphisms, equivalence relations Page 45: Exercises (2)–(5)
Oct 14 2.5 Equivalence relations, partitions Page 45: Exercise (7)
Oct 18 2.6, 2.7 Quotient vector spaces, the first isomorphism theorem Page 48: Exercises (1)–(6); Page 50: Exercises (1)–(6)
Oct 21 Midterm exam (covers material up to and including lecture of October 18)
Nov 1 3.1–3.3 Generating sets, linear dependence/independence Page 54: Exercises (1)–(4); Page 57: Exercises (3)–(5), (7), (8); Page 59: Exercises (1)–(7), (12)
Nov 4 3.3, 3.4 Linear dependence/independence, finitely generated vector spaces Page 59: Exercises (9), (11), (13); Page 65: Exercises (1), (4), (6)
Nov 8 3.4, 3.5 Basis Page 65: Exercise (7); Page 71: Exercises (1)–(3), (5)–(8), (11), (13), (18)
Nov 11 3.5 Dimension Page 71: Exercises (9), (10), (12), (14), (20)
Nov 15 3.6–3.8 Conservation of dimension, dimensions of spaces of linear maps Page 76: Exercises (1)–(5), (7)–(12), (14); Page 80: Exercises (3), (6), (7); Page 83: Exercises (2), (3), (7), (8), (10)
Nov 18 3.9 Student course evaluations. Linear functionals and dual spaces Page 89: Exercises (2), (3), (5)–(7), (10), (12), (13)
Nov 22 4.1–4.9 Matrices Page 101: Exercises (1)–(5), (7)–(12)
Nov 25 4.10 Change of basis, similar matrices, inner product spaces Page 128: Exercises (2), (3), (6)–(8)
Nov 29 5.1 Orthogonality, Gram-Schmidt algorithm Page 135: Exercises (1), (3)–(9)
Dec 2 5.2–5.4 Discussion of final exam. Duality revisited, adjoints Page 140: Exercises (1), (2), (4), (6), (7); Page 146: (1), (3), (4), (7)
Dec 6 6.4–6.7 Characteristic polynomials, diagonalizing symmetric matrices Page 171: Exercises (1)–(3); Page 176: Exercise (1); Page 181: Exercise (1)
Dec 8 N/A Review N/A

* The exercises listed here are always in addition to the exercises written in the lecture notes.

Notes

Below are lecture notes for the course. They are a single file that will be updated after each lecture. Please keep in mind that these are notes that the professor writes for himself when preparing the lecture and should be complemented by a student's own class notes. Often more will be said in class than is in the notes. If you notice any errors in these notes (even small typos), please inform the professor. This helps him as well as your fellow students.