Class
| lecture | tutorial | |
| Time | Wed, Fri | Tue |
| 13:30 - 14:50 | 20:00 - 20:50 | |
| Venue | 2504 | 2406 |
| Instructor | YAN Min | |
| Office | 3487 | |
| Phone | 23587442 | |
Prerequisite
Basic geometrical imagination, solving systems of linear equations, basic knowledge of polynomials.
Topics
Vector Space
linear combination, span, linear independence, system of linear equations, row echelon form, basis, coordinate, dimension
Linear Transformation
linear transformation, composition, matrix operation, one-to-one, onto, isomorphism, matrix of linear transformation, change of basis
Subspace
span, range, rank, kernel, sum, direct sum, projection, blocks of linear transformation, quotient space, direct summand
Inner Product
dot product, inner product, adjoint, orthogonality, orthonormal basis, isometry, orthogonal matrix, Gram-Schmidt, orthogonal complement, orthogonal projection, complementarity principal
Determinant
determinant of square matrix, permutation, row and column operation on determinant, cofactor expansion, determinant of linear operator, orientation, volume
Advanced Vector Space
complex number, complex inner product, complex vs real structure, module over ring, abelian group, polynomial
Eigenvalue and Eigenvector
eigenspace, characteristic polynomial, diagonalization, normal operator, hermitian operator, unitary operator
Spectral Theory
invariants of linear operator, Cayley-Hamilton Theorem, algebraic and geometric multiplicity, invariant subspace, Jordan canonical form, minimal polynomial, other canonical forms
Tensor
bilinear function, quadratic form, signature, positive definite, multilinear function, tensor of vector space, exterior algebra
Homework
No hard copies of the homework will be distributed. Please check my web page for the latest assignments. Usually you have one week to do the homework. The answer will be put on my web page after the homework is collected. Absolutely no late homework will be accepted.
Exam and Grade
Homework 20%, midterm 30%, final 50%.
Note
The syllabus is subject to change as circumstances arise.