Linear Algebra II

Academic Year 2022 - 2023
Semester 1

NUSMods Description

This module is a continuation of MA1101 Linear Algebra I intended for second year students. The student will learn more advanced topics and concepts in linear algebra. A key difference from MA1101 is that there is a greater emphasis on conceptual understanding and proof techniques than on computations. Major topics: Matrices over a field. Determinant. Vector spaces. Subspaces. Linear independence. Basis and dimension. Linear transformations. Range and kernel. Isomorphism. Coordinates. Representation of linear transformations by matrices. Change of basis. Eigenvalues and eigenvectors. Diagonalizable linear operators. Cayley-Hamilton Theorem. Minimal polynomial. Jordan canonical form. Inner product spaces. Cauchy-Schwartz inequality. Orthonormal basis. Gram-Schmidt Process. Orthogonal complement. Orthogonal projections. Best approximation. The adjoint of a linear operator. Normal and self-adjoint operators. Orthogonal and unitary operators.


This module is taught by Prof Zhang Deqi. He (haiiizz) is the prof who has the most ASMR voice ever. He just reads off the notes and goes at breakneck speed. Can I also say, the proofs he wrote are almost unreadable due to his handwriting? As a result, before midterms, I spent an entire weekend proving 107 theorems all by hand so that it can help me for revision for the Finals. I gave up going to lectures after midterm but I still attempt and attend tutorials.

There are 5 homework problems (easy), a midterm and a final. I got careless for 1 question in the midterm (scored 79% for the midterm which is below median) due to me misinterpreting a question. I think the final was easy which killed me a bit because everyone would have done very well. Ended up with a disgraceful B+ (probably caused by midterm)

This module is really wasted. I was very much looking forward to learning more about Linear Algebra but Prof Zhang made it super dull and almost impossible to follow I realised (albeit too late), that attending lectures was counterproductive and I am better off studying the module by myself, which is possible as I am confident with my mathematical ability. I should have applied for the 5MC S-version instead. It is harder, but it will be worth it. I don’t need a prof who adds to my workload unnecessarily.