Course - Linear Algebra II HT23

Created: January 14, 2023 | Updated: October 13, 2025 | Read markdown | About these notes | View in context | Study these flashcards

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This follows on from the definitions and results in Course - Linear Algebra MT22^U, first introducing the determinant and then the concept of eigenvalues and eigenvectors. It then introduces the notion of diagonalisability, and then proves the “spectral theorem” for real symmetric matrices in an inner product space, which means that every real symmetric matrix is diagonalisable.

This was a really good course, it was lectured by James Maynard which was fun since he won the Fields Medal in 2022. It did feel like this meant like a lot of people in the lectures were taking every chance they could to correct any mistakes. In the final lecture he turned it into a game by keeping score like it was football – every time someone pointed out a mistake, it was one point for the audience, and every time someone mis-corrected him it was one point for him.

• Course Webpage
• Lecture Notes
• Related courses:
  • Successor to: Course - Linear Algebra MT22^U
  • Predecessor to: Course - Linear Algebra MT23^U
• Other courses this term: Courses HT22^U

Notes

• Notes - Linear Algebra II HT23, Determinants^U
• Notes - Linear Algebra II HT23, Eigenvectors and eigenvalues^U
• Notes - Linear Algebra II HT23, Gram-Schmidt Process^U
• Notes - Linear Algebra II HT23, Matrix multiplication^U
• Notes - Linear Algebra II HT23, Permutations^U
• Notes - Linear Algebra II HT23, Quadrics^U
• Notes - Linear Algebra II HT23, Spectral Theorem^U
• Notes - Linear Algebra II HT23, Trace^U
• Notes - Linear Algebra II HT23, Misc^U

Lectures

• Lecture - Linear Algebra II HT23, I^U
• Lecture - Linear Algebra II HT23, II^U
• Lecture - Linear Algebra II HT23, III^U
• Lecture - Linear Algebra II HT23, IV^U
• Lecture - Linear Algebra II HT23, V^U
• Lecture - Linear Algebra II HT23, VI^U
• Lecture - Linear Algebra II HT23, VII^U
• Lecture - Linear Algebra II HT23, VIII^U

Problem Sheets

• Sheet 1
• Sheet 2
• Sheet 3
• Sheet 4

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