Both sessions will cover the same materials. You are free to attend one or both of them.
Pages for 2017 Fall, 2016 Fall (WARNING : The notes that I am using this year may not be identical to previous years. They are here for your reference)
Tutorial Sheets:
Tutorial 1 - Linear Independence, Span, Basis Inequality, TFAE Theorem Ver 0.5
Tutorial 2 - Subspaces, Transition Matrices, Spaces of Polynomials (Dimensions and Basis) [Video Solution to Q8(c)]
Tutorial 3 - Linear maps, Linear maps of Polynomials, Rank and Nullity Theorem
Tutorial 4 - More on Rank and Nullity: Rank Inequalities, QAP Theorem and its application
Reading Week (Ver 2018) - Linear Maps : Computing Kernels, Image, Rank-Nullity, TFAE Theorem Final, many more examples
Tutorial 5 - Systems of Equations, Determinants and their Laplace expansions
Tutorial 6 - Similarity, Diagonalisation algorithm, Diagonalisation I: Existence of "Eigenbasis"
Tutorial 7 - Diagonalisation II: Alg. & Geom. multiplicities, Cayley-Hamilton theorem, Algorithm for minimal polynomials
Extra reading - Similar matrices and their properties
Tutorial 8 - Diagonalisation III: Minimal Polynomial, Divisibility Lemma for Min Poly, Spectrum Theorems 1 : Inner Product Space
[Completed version available here due to the fire alarm]
Tutorial 9 - (Substituted by Momchil Konstantinov) Spectrum Theorems 2: Orthonormal Basis, Unitary, Normal and Self-adjoint Matrices, (Real Story) Orthogonal matrices
Tutorial 10 Spectrum Theorems 3: Orthonormal Basis by Gram-Schmidt Process, Unitarily Diagonalisable if and only if Normal