Linear Algebra (MAST10007_2022_SM2)
https://lms.unimelb.edu.au/canvas
Subject Coordinator: Dr Christine Mangelsdorf, mangel@unimelb.edu.au
Lecture
Monday, Wednesday, Friday, 10am-11:00am in the JH Michell theatre, Peter Hall building
Monday 11:00am-12:00pm, Peter Hall-G14
Friday 11:00-12:00pm, Peter Hall-G70 (Wilson Laboratory)
Wednesday: 11:00am-12:30pm
Thursday: 1:30pm-3:00pm
The approximate lecture schedule for MAST10007 Linear Algebra is shown in the table below. The content of each lecture may vary slightly.
Section 1: Linear Equations
Lecture 1 - Systems of linear equations. Row operations.
Lecture 2 - Reduction of systems to row-echelon form and reduced row-echelon form.
Lecture 3 - Consistent and inconsistent systems.
Section 2: Matrices and Determinants
Lecture 4 - Matrix operations. Matrix inverses.
Lecture 5 - Matrix inverses. Elementary matrices.
Lecture 6 - Elementary matrices. Rank of a matrix. Linear systems revisited.
Lecture 7 - Determinants using row operations and cofactors.
Section 3: Euclidean Vector Spaces
Lecture 8 - Vectors in Rn. Dot product. Cross product.
Lecture 9 - Cross product. Scalar triple product. Lines.
Lecture 10 - Lines. Planes.
Section 4: General Vector Spaces
Lecture 11 - General vector spaces - real, complex, polynomials, matrices, functions.
Lecture 12- Subspaces - real, complex, polynomials, matrices, functions.
Lecture 13 - Linear dependence and independence.
Lecture 14 - Linear dependence and independence.
Lecture 15 - Spanning sets.
Lecture 16 - Bases and dimension.
Lecture 17 - Bases and dimension. Solution space.
Lecture 18 - Solution space, column space and row space.
Lecture 19 - Rank-nullity theorem. Coordinates relative to a basis.
Section 5: Linear Transformations
Lecture 20 - General linear transformations.
Lecture 21 - Geometric linear transformations from R2 to R2.
Lecture 22 - Matrix representations for general linear transformations.
Lecture 23 - Image, kernel, rank and nullity.
Lecture 24 - Invertible linear transformations. Change of basis.
Lecture 25 - Change of basis.
Section 6: Eigenvalues and Eigenvectors
Lecture 26 - Definition of eigenvalues and eigenvectors. Finding eigenvalues.
Lecture 27 - Finding eigenvectors.
Lecture 28 - Diagonalisation of matrices over R and C.
Lecture 29 - Matrix powers. Markov Chain example.
Section 7: Inner Product Spaces
Lecture 30 - Definition of inner products. Hermitian dot product on Cn.
Lecture 31 - Geometry from inner products.
Lecture 32 - Orthogonal sets and Gram-Schmidt procedure.
Lecture 33 - Least squares curve fitting. Orthogonal matrices.
Lecture 34 - Orthogonal matrices. Symmetric matrices. Singular value decomposition.
Lecture 35 - Unitary matrices. Hermitian matrices.