# Course - Linear Algebra MT23

> Source: https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/ · Updated: 2025-09-30 · Tags: uni, course

> Part A course that continues on from the Prelim courses [Course - Linear Algebra MT22](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/) and [Course - Linear Algebra II HT23](https://ollybritton.com/notes/uni/prelims/ht23/linear-algebra/). Introduces the minimal polynomial, the primary decomposition theorem, Jordan normal form, dual spaces, adjoints, and complex inner product spaces.

- [Course Webpage](https://courses.maths.ox.ac.uk/course/view.php?id=4972)
- [Lecture Notes](https://courses.maths.ox.ac.uk/pluginfile.php/30064/mod_resource/content/2/A0.pdf)
- Previous linear algebra courses:
	- [Course - Linear Algebra MT22](https://ollybritton.com/notes/uni/prelims/mt22/linear-algebra/)
	- [Course - Linear Algebra II HT23](https://ollybritton.com/notes/uni/prelims/ht23/linear-algebra/)
- Other courses this term: [Courses MT23](https://ollybritton.com/notes/uni/part-a/mt23/)

### Problem Sheets
- [Sheet 1](https://courses.maths.ox.ac.uk/pluginfile.php/30060/mod_assign/introattachment/0/quest1A0.pdf)
- [Sheet 2](https://courses.maths.ox.ac.uk/pluginfile.php/30061/mod_assign/introattachment/0/quest2A0.pdf)
- [Sheet 3](https://courses.maths.ox.ac.uk/pluginfile.php/30062/mod_assign/introattachment/0/quest3A0.pdf)
- [Sheet 4](https://courses.maths.ox.ac.uk/pluginfile.php/30063/mod_assign/introattachment/0/quest4A0.pdf)

### Notes
- [Notes - Linear Algebra MT23, Integral domains](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/integral-domains/)
- [Notes - Linear Algebra MT23, Rings](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/rings/)
- [Notes - Linear Algebra MT23, Fields](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/fields/)
- [Notes - Linear Algebra MT23, Homomorphisms](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/homomorphisms/)
- [Notes - Linear Algebra MT23, Rank-nullity theorem](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/rank-nullity-theorem/)
- [Notes - Linear Algebra MT23, Quotient spaces](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/quotient-spaces/)
- [Notes - Linear Algebra MT23, Minimal polynomials](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/minimal-polynomials/)
- [Notes - Linear Algebra MT23, Cayley-Hamilton theorem](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/cayley-hamilton-theorem/)
- [Notes - Linear Algebra MT23, Triangular form theorem](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/triangular-form-theorem/)
- [Notes - Linear Algebra MT23, Primary decomposition theorem](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/primary-decomposition-theorem/)
- [Notes - Linear Algebra MT23, Dual spaces](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/dual-spaces/)
- [Notes - Linear Algebra MT23, Annihilators](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/annihilators/)
- [Notes - Linear Algebra MT23, Inner product spaces](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/inner-product-spaces/)
- [Notes - Linear Algebra MT23, Adjoints](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/adjoints/)
- [Notes - Linear Algebra MT23, Invariant subspaces](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/invariant-subspaces/)
- [Notes - Linear Algebra MT23, Orthogonal complements](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/orthogonal-complements/)
- [Notes - Linear Algebra MT23, Jordan normal form](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/jordan-normal-form/)
- [Notes - Linear Algebra MT23, Orthogonal sets](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/orthogonal-sets/)
- [Notes - Linear Algebra MT23, Orthogonal and unitary transformations](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/orthogonal-and-unitary-transformations/)
- [Notes - Linear Algebra MT23, Misc](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/notes/misc/)

### Lectures
- [Lecture - Linear Algebra MT23, I](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/i/)
- [Lecture - Linear Algebra MT23, II](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/ii/)
- [Lecture - Linear Algebra MT23, III](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/iii/)
- [Lecture - Linear Algebra MT23, IV](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/iv/)
- [Lecture - Linear Algebra MT23, V](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/v/)
- [Lecture - Linear Algebra MT23, VI](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/vi/)
- [Lecture - Linear Algebra MT23, VII](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/vii/)
- [Lecture - Linear Algebra MT23, VIII](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/viii/)
- [Lecture - Linear Algebra MT23, IX](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/ix/)
- [Lecture - Linear Algebra MT23, X](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/x/)
- [Lecture - Linear Algebra MT23, XI](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/xi/)
- [Lecture - Linear Algebra MT23, XII](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/xii/)
- [Lecture - Linear Algebra MT23, XIII](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/xiii/)
- [Lecture - Linear Algebra MT23, XIV](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/xiv/)
- [Lecture - Linear Algebra MT23, XV](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/xv/)
-  [Lecture - Linear Algebra MT23, XVI](https://ollybritton.com/notes/uni/part-a/mt23/linear-algebra/lectures/xvi/)

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