David Aristoff's homepage
Office hours: MW 10:50-11:50, Tues 12:00-1:00, Weber Hall 221
For a free version of our textbook, see
A textbook with a different flavor (but also free) can be found here.
You can bring 3 pages of notes, each with writing only on one side, to the final exam.
Week 1 concepts: systems of linear equations, matrices, vectors, REF and RREF ---- see chapters SSLE and RREF
Week 2 concepts: homogeneous systems of equations, matrix multiplication, matrix inverses and identity ---- see chapters HSE, NM and MM
Week 3 concepts: linear combinations, span, vector spaces, solution sets of linear equations ---- see chapters LC and SS
Week 4 concepts: linear independence, basis, dimension, linear maps ---- see chapters LI, B and D
Week 5 concepts: rank-nullity theorem,
coordinates with respect to bases, composition of linear maps, matrix multiplication ---- see chapter MM
Week 6 concepts: symmetric matrices, length, angle, orthogonality,
orthogonal matrices -- see chapters O and MO
Week 7 concepts: determinants, characteristic polynomial, eigenvalues/eigenvectors -- see chapters DM and EE
Week 8 concepts: eigenspaces, multiplicities of eigenvalues, minimal polynomial, diagonalization -- see chapter EE
Week 9 concepts: orthogonality, orthogonalization, Gram-Schmidt --- see chapter O
Week 10 concepts: orthonormal sets, QR factorization, applications
Week 11 concepts: QR factorization, Householder reflections
Week 12 concepts: review, applications, examples
Homework 1 (due Friday Sept 5): Section RREF, C30-C33; Section TSS, C22, C24, C26, C28, M51-M57
Homework 2 (due Friday Sept 12): Section HSE, C21-C23, C25-C27, M50-M52; Section NM, C30-C33, M30, M51-M52, T30
Homework 3 (due Friday Sept 19): Section LC, Reading questions 1-3, C40; Section SS, Reading questions 1-2, C40-C45, M10, M11, M12
Homework 4 (due Friday Sept 26): Section LI, Reading questions 1-3, C20-C25; Section LDS, C50-C52; and
Homework 5 (due Friday Oct 10): these problems.
Homework 6 (due Friday Oct 17): Section O, Reading questions 1-2, M60, T20; Section MO, T34; Section DM, C21, C23, C26, and these problems.
Homework 7 (due Friday Oct 24): Section EE, C10-C12, C19-C20, C23-C27, and these problems.
Homework 8 (due Friday Nov 14): these problems.
Homework 9 (due Friday Nov 21): these problems.
Homework 10 (due Friday Nov 28): these problems.
Solutions to Midterm 1
Solutions to Midterm 2
Solutions to Midterm 3