All references are to the course textbook (Friedberg-Insel-Spence), by chapter and section, unless otherwise specified.

Daily readings are to be completed prior to the specified class period; daily problems are to be completed after the specified class period and before the subsequent class period.

Date	Topics covered	Daily reading	Daily problems	Remarks
1/14	Introduction to linear algebra			Welcome to Math 416!
1/16	Systems of linear equations, elementary row operations, row echelon form, Gauss elimination	III.4	III.4 #2(a)(b)(e)
1/18	Matrix arithmetic, elementary matrices, pivots, rank	III.1, III.2
1/21	NO CLASS			MLK Day
1/23	Invertibility, matrix inverses	III.2		Guest lecturer: Prof. D'Angelo
1/25	Systems of linear equations, polynomial interpolation, definition of a vector space	I.2	I.2 #1,17	Homework #1 due
1/28	Subspaces	I.3
1/30	Span of a set, linear dependence and independence	I.4, I.5	I.3 #11, I.4 #17
2/1	Bases, dimension	I.6	I.6 #1(a)(b)(c)(d)(e)
2/4	Bases, dimension (continued)	I.6		Homework #2 due
2/6	Existence of bases for general vector spaces, examples	I.7
2/8	Linear transformations	II.1
2/11	Kernel, range, Rank-Nullity theorem	II.1	II.1 #19: give an example where T and U are linearly independent
2/13	Matrix representation of a linear transformation	II.2		Homework #3 due
2/15	Composition of transformations and matrix multiplication	II.3
2/18				MIDTERM EXAM #1 (CHAPTERS 3 AND 1)
2/20	Dual spaces	II.6		Guest lecturer: Prof. D'Angelo
2/22	Dual spaces (continued)	II.6		Guest lecturer: Prof. D'Angelo
2/25	Bilinear functions	IV.1, Handout
2/27	Multilinear functions, determinants	IV.2, IV.3, IV.5		Homework #4 due
2/29	Multiplicativity, geometry of determinants	IV.1, IV.3
3/3	Similarity of matrices, eigenvalues and eigenvectors	II.5, V.1
3/5	Eigenvalues and eigenvectors (continued), characteristic polynomial	V.1, V.2	Prove that trace(AB) = trace(BA) Prove that determinant and trace are similarity invariants for nxn matrices
3/7	Eigenvalues and eigenvectors (continued), characteristic polynomial	V.1, V.2		Homework #5 due
3/10	Diagonalizability, review for Midterm Exam #2	V.2		Practice Problems for Exam #2
3/12				MIDTERM EXAM #2 (CHAPTERS 2 AND 4)
3/14	Linear algebra and differential equations	II.7, V.2
3/24	Inner products and norms	VI.1
3/26	Cauchy-Schwarz inequality, triangle inequality, orthonormal bases	VI.1, VI.2
3/28	Gram-Schmidt, orthogonal complements, existence of distance minimizers for finite-dimensional subspaces	VI.2
3/31	Adjoint of a linear operator, Riesz Representation Theorem (finite-dimensional case)	VI.3
4/2	Least squares approximation	VI.3
4/4	Normal operators	VI.4		Homework #6 due
4/7	Self-adjoint operators, simultaneous diagonalization	VI.4
4/9	Unitary and orthogonal operators, geometry of Euclidean rigid motions	VI.5, VI.11
4/11	Spectral Decomposition Theorem (finite-dimensional case)	VI.6
4/14	Singular values and polar decomposition	VI.7		Homework #7 due
4/16	Examples
4/18				MIDTERM EXAM #3 (SECTIONS 5.1, 5.2, 6.1, 6.2, 6.3, 6.4)
4/21	Cayley-Hamilton theorem, cyclic and invariant subspaces	V.5
4/23	Minimal polynomials	VII.3
4/25	Jordan canonical form	VII.1
4/28	Jordan canonical form (continued)	VII.1, VII.2
4/30	Review for the final exam			Homework #8 due Review Sheet and Practice Problems for the Final Exam
5/5	FINAL EXAM 1:30-4:30 IN 343 ALTGELD HALL

Homework assignments

Homework 1: due Friday, January 25

Homework 2: due Monday, February 4

Homework 3: due Wednesday, February 13

Homework 4: due Wednesday, February 27

Homework 5: due Friday, March 7

Homework 6: due Friday, April 4

Homework 7: due Monday, April 14

Homework 8: due Wednesday, April 30