Math 245: Linear Algebra 2, Advanced Section (University of Waterloo, Winter 2009)

Course Outline

Coordinates

Instructor

Announcements

• Assignment 10 has been graded and is available outside MC 4031.
• The solution to Assignment 9, question 1b has been corrected.
• On Assignment 8, question 1, you should assume that T = ∑_j λ_jP_j is the spectral decomposition of T. Also, in part b, both sums should be from j = 0 to ∞.
• On Assignment 5, question 2d, you should also assume that D is regular.
• On Assignment 4, question 4c, you should find an invertible matrix S such that S^-1AS, S^-1DS are both diagonal, not S^-1AS, S^-1BS. Also, in question 5, a permutation matrix has exactly one 1 in each row and in each column.
• On Assignment 1, question 2, T should be a linear transformation from V ⊗ V to itself, not from V to itself.
• Office hours will not be held on 12 or 13 January. Please send any questions that arise by email; you can expect a prompt reply.

Schedule

Notes

• Proof that the tensor product is basis-independent
• Comparison of direct sums and tensor products
• Solving a system of differential equations using eigenvalues and eigenvectors
• Final exam review