Advanced Linear Algebra

Advanced Linear Algebra

Vladimir Ivanov

Intoductory notes 1 – Maps of Sets

Intoductory notes 2 – Equivalence Relation

Intoductory notes 3 – Groups and Fields

Lecture 1 – Vector spaces

Lecture 2 – Basis, Dimension

Lecture 3 – Linear Maps

Lecture 4 – Matrices of Linear Maps

Lecture 5 – Dual Spaces and Tensor Products

Lecture 6 – Symmetric and Exterior Powers, Determinant

Lecture 7 – Characteristic Polynomial

Lecture 8 – Eigenvalues and Eigenvectors

Lecture 9 – Jordan Canonical Form Theorem

Lecture 10 – Complexification, Jordan Canonical Form for the Real Case

Lecture 11 – Inner product spaces

Lecture 12 – Operators in an Inner Product Space

Recommended textbooks

1. S. Friedberg, A. Insel, L. Spence, Linear Algebra.
2. S. Axler, Linear Algebra Done Right.
3. S. Roman, Advanced Linear Algebra

I’d be truly grateful for any comments, suggestions, typo corrections, or error reports you might share. Please feel free to send them to vivanov@mathinmoscow.org.