MTH6140 - Linear Algebra II - 2023/24
Topic outline
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Forum Description: This forum is available for everyone to post messages to, but aimed mainly at students to discuss amongst themselves. Thus, students are encouraged to post to this forum and should feel free to reply to other students if they are able to.
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This is an external YouTube link to a fun tutorial of which the first 1/2 hour is mostly revision of the level of Linear Algebra I. Ignore the bit about \(L^p\) norms as that will be too advanced for now, but we will touch upon \(L^2\) but the end of our course. The full tutorial is intended for people working in neural networks, so do ignore the last part ... or keep watching for a bit fun to see linear algebra in action in the real world.
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This was an on-campus exam from before the pandemic and your January exam will have a broadly similar format..
We will go through this exam in the introductory lecture but consider doing it yourself and marking it to see how you are at the start of the module. Try the same at the end of the module in December!
Also revise Linear Algebra I in any areas of weakness that you find when we look through this exam and/or check out this YouTube tutorial below.
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Modern thinking is to have a go at the exam at the start of the course, expect to fail, have a look at the solutions which will be puzzling at this stage, then repeat the process at the end of the course. (I will also make some previous years and their solutions available for revision.)103.3 KB
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Covers material from Weeks 1-2
Solutions will be automatically visible once the deadline expires. This also means that its not possible to allow answers after the deadline.
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This covers material from Weeks 3 and 4.
Solutions will be automatically visible once the deadline expires. This also means that its not possible to allow answers after the deadline.
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Covers material from Weeks 5 and 6
Solutions will be automatically visible once the deadline expires. This also means that its not possible to allow answers after the deadline.
Due to the week 7 break this is actually due two weeks later from when it goes live.
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Covers material from Weeks 8,9
Solutions will be automatically visible once the deadline expires. This also means that its not possible to allow answers after the deadline.
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Covers mainly material from Weeks 10, 11 and possibly first lecture of Week 12
Solutions will be automatically visible once the deadline expires. This also means that its not possible to allow answers after the deadline.
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This module is a mixture of abstract theory, with rigorous proofs, and concrete calculations with matrices. The abstract component builds on the theory of vector spaces and linear maps to construct the theory of bilinear forms (linear functions of two variables), dual spaces (which map the original space to the underlying field) and determinants. The concrete applications involve ways to reduce a matrix of some specific type (such as symmetric or skew-symmetric) to as near diagonal form as possible.
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The module is taught by Professor Shahn Majid (s.majid@qmul.ac.uk) with teaching assistance for Tutorials provided by Itamar Mor (i.a.mor@qmul.ac.uk)
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- I advise each week to read the assigned pages of the Printed Lecture Notes. Make good notes – don’t just highlight .
- Try to do this in a first look form before the Lecture and review it again after the relevant lecture. You can also browse books and online resources to enhance your understanding of the week’s topic.
- Bring the printed courseworks to the weekly tutorial and try to solve them (and/or understand the provided solutions).
- Identify any other questions to bring to the coursework tutorial (or to my office hour if you want).
- You are allowed to ask questions on looking at the quiz but we can't give hints to solutions for upcoming quiz, only general advice.
- You can also email me if your query is super-specific (eg including a page and line number)
- I advise each week to read the assigned pages of the Printed Lecture Notes. Make good notes – don’t just highlight .
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Come to the Q&A tutorial sessions or come by my advertised Learning Support Hour). You can also email for help, but be as precise as possible about your issue.
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DOWNLOAD THIS for use throughout the course. My live lectures will be supplementary to this
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There is non-assessed coursework with solutions in the weekly topic blocks on the Module Content tab. This complements the in-term Quizzes which are the assessed element of coursework for the module.
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Below you can find many past exams and their solutions at least in outline form sufficient for self-marking. The designated Sample Exam which we went through in detail during the lectures starting in week 1 was the May 2019 exam which is also below along with its solutions (as well as these posted in week 1).
You can also search the QMPLUS repository for past exams
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