Last Year Webpage: Here
Warning: I am not using exactly the same set of tutorial notes this year. They are here for your references.
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)
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 Applications
Reading Week - Linear Maps : Computing Kernels, Image, Rank-Nullity, TFAE Theorem Ver 1
Tutorial 5 - Systems of Equations, Determinants, Laplace Expansion
Tutorial 6 - Similarity, Diagonalisation Algorithm, Diagonalisation I: Existence of "Eigenbasis"
Tutorial 7 - Diagonalisation II: Alg. & Geom. Multiplicities, Cayley-Hamilton Theorem, Minimal Polynomial(Algorithm)
Tutorial 8 - Diagonalisation III: Minimal Polynomial, Divisibility Lemma for Min Poly, Spectrum Theorems 1 : Inner Product Space
Tutorial 9 - 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