Class Resources for MATH/MTHE 212: Linear Algebra-II at Queen's University in Winter 2018
Class Resources for MATH/MTHE 212: Linear Algebra-II at Queen's University in Winter 2018
Week 1 :
Topics: Vector spaces, subspaces, sums and direct sums.
No tutorial in Week 1 .
Week 2 :
Topics: Span, Linear Independence and Basis of a Vector Space.
Summary of Week 2 which contains details of proofs that were skipped/sketched in class.
Week 2 Tutorial.
Week 3 :
Topics: Dimension, Linear maps, Kernel and Image of linear maps
Week 3 Tutorial.
Week 4 :
Topics: Matrix of a linear map, Invertible linear maps, Invariant subspaces.
Week 4 Tutorial.
Week 5:
Topics: Upper triangular matrices, Diagonal matrices, Inner Product spaces.
Week 5 Tutorial.
A checklist to help you prepare for the midterm.
Week 6 :
Topics:Norms, orthonormal vectors, Gram-Schmidt process.
Week 6 Tutorial.
Week 7 :
Topics:Orthogonal projections, minimizing distance, method of least squares, adjoints.
Notes on least squares solutions given in the summary notes.
Week 7 Tutorial.
Week 8 :
Topics:Self-adjoint operators, Normal operators, Spectral theorems, Positive operators, Isometries.
Week 8 Tutorial.
Week 9 :
Topics: Finding square roots of positive operators, Polar Decomposition and Singular Value Decomposition.
Week 9 Tutorial.
Week 10 :
Topics: Generalized eigenvectors, multiplicity of an eigenvalue, Characteristic and minimal polynomials
Week 10 Tutorial.
Week 11 :
Topics: Decomposition of operators (contd.), Jordan Forms
Week 11 Tutorial.
Week 12 :
Topics: Jordan Forms problems, applications of SVD (won't be tested) and Review.
Week 12 Tutorial.
Write-up for Polar decomposition using SVD.
Exam preparation :