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# NUS Math Module Review: MA4230 Matrix Computation

Assessment:

Midterms: 25% (75 mins test, I got 48/50, mean was 39/50)

Tutorial participation: 5% (just show up twice and present some tutorial solutions)

Finals: 70%

This module was quite a breeze to me, probably because I liked linear algebra related modules and had done well in them previously. This module focused on developing algorithms to compute eigenvalues/singular values and eigenvectors/ singular vectors. It was done by introducing various matrix decomposition/factorisation, like Singular Value Decomposition (SVD), QR factorisation, Schur factorisation etc and subsequently theorems and algorithms were developed to compute the eigenvalues and eigenvectors by applying the matrix decomposition in different ways.

The Householder transformation was used almost throughout the lectures after the mid-terms but wasn’t formally introduced in the notes so I had to read it up on my own, it turned out to be a pretty intuitive and useful concept. I think knowing how the Householder transformation works in the general case was a differentiating factor between the A’s and B+’s. I reckon the majority of the cohort still don’t understand how this technique works, as evident from the tutorial presentations I sat through, and also my A+ even though I didn’t think I did that well.

The finals wasn’t that difficult, the bulk of the exam was computational, and the proving questions were similar to the tutorial ones. I was quite diligent in completing the tutorials independently, so I could easily replicate the answers to some of the similar questions during finals. I couldn’t prove a theorem resembling the Bauer-Fike Theorem worth 4 marks and got stumped by a computational QR algorithm question due to my lack of understanding of the algorithm. Somehow I still managed to get A+, I guess the rest of the cohort understood less about the module content than I already did.

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