Advanced Linear Algebra
Vladimir Ivanov
Syllabus of the course
Intoductory notes 1 – Maps of sets
Intoductory notes 2 – Equivalence Relation
Intoductory notes 3 – Groups and Fields
Lecture 1 notes – Vector spaces; Problem Set 1
Lecture 2 notes – Basis, Dimension; Problem Set 2
Lecture 3 notes – Linear Maps; Problem Set 3
Lecture 4 notes – Change of Basis; Problem Set 4
Lecture 5 notes – Tensor Products
Lecture 6 notes – Symmetric and Exterior Powers; Problem Set 5-6
Lecture 7 notes – Characteristic Polynomial, Cayley-Hamilton Theorem; Problem Set 7
Lecture 8 notes – Eigenvalues and Eigenvectors, Primary Decomposition Theorem; Problem Set 8
Lecture 9 notes – Jordan Canonical Form Theorem; Problem Set 9
Lecture 10 notes – Complexification, Jordan Form for the Real Case
Lecture 11 notes – Inner product spaces; Problem Set 11
Lecture 12 notes – Operators in an Inner Product Space; Problem Set 12
Recommended textbooks
- S. Friedberg, A. Insel, L. Spence, Linear Algebra.
- S. Axler, Linear Algebra Done Right.
- S. Roman, Advanced Linear Algebra
Additional resources.
- Youtube Linear Algebra course by Professor Steven Roman
- Youtube Advanced Linear Algebra course by Professor Matthew Macauley