MATH 252
Linear Algebra II
Winter 2026
Topics
- Complex numbers
- Eigenvalues and Eigenvectors
- Diagonalization
- Standard Inner product
- Orthogonality. Orthogonal/normal bases.
- Projections and Gram-Schmidt process
- Least squares
- The adjoint of a Linear Operator
- Isometries: unitary and orthogonal matrices
- Rigid motions in Rn
- Schur triangular representation
- Normal and Self-Adjoint Operators
- Positive definite operators
- Singular values decompositions
- Applications of SVD
- Quadratic forms
- Diagonalization of Quadratic Forms
- Positive definite forms and Sylvester criterion
- The Cayley-Hamilton Theorem
- The minimal polynomial
- Jordan Canonical Form
Readings
- Sergei Treil. Linear Algebra Done Wrong. https://www.math.brown.edu/~treil/papers/LADW/LADW_2025_08-25.pdf
Winter 2024 · MATH 252
Readings
- Linear Algebra Done Wrong, by Sergei Treil.
Winter 2023 · MATH 252
Readings
- Linear Algebra, 5th Edition, by Friedberg, Insel & Spence, Prentice Hall.
Winter 2022 · MATH 252
Readings
- Linear Algebra, 5th Edition, by Friedberg, Insel & Spence, Prentice Hall.
Sources
- Course catalogue ↗2026–2027
- Syllabus or course outline ↗Winter 2026
- Historical course outline ↗Winter 2024
- Historical course outline ↗Winter 2023
- Historical course outline ↗Winter 2022
- Winter 2026 outline.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.
- Historical source. Generic Textbook/References headings remain requirement-unspecified. Bibliographic editions and years are retained as printed; source inconsistencies may remain. Automated extraction with conservative filtering; distinct bibliography strings screened for false positives; entire syllabus not manually reviewed.