MATH 245
Linear Algebra 2 (Advanced Level)
Undated · Linear Algebra2
Topics
- Affine Spaces, Convex Sets and Simplices
- The Dot Product and Orthogonal Projections
- Applications of Orthogonal Projection
- The Generalized Cross Product
- Inner Products
- Orthogonal Bases and Orthogonal Projection
- The Dual and Adjoint of a Linear Map
- Orthonormal Diagonalizations
- Bilinear Forms
- Quadratic Forms
- Tensor Algebras (Optional)
- Jordan Canonical Form
Readings
- Chapter 1. Affine Spaces, Convex Sets and Simplices — https://www.math.uwaterloo.ca/~snew/MATH245/Chap1AffineSpaces.pdf
- Chapter 2. The Dot Product and Orthogonal Projections — https://www.math.uwaterloo.ca/~snew/MATH245/Chap2DotProduct.pdf
- Chapter 3. Applications of Orthogonal Projection — https://www.math.uwaterloo.ca/~snew/MATH245/Chap3ProjectionApplications.pdf
- Chapter 4. The Generalized Cross Product — https://www.math.uwaterloo.ca/~snew/MATH245/Chap4CrossProduct.pdf
- Chapter 5. Inner Products — https://www.math.uwaterloo.ca/~snew/MATH245/Chap5InnerProducts.pdf
- Chapter 6. Orthogonal Bases and Orthogonal Projection — https://www.math.uwaterloo.ca/~snew/MATH245/Chap6OrthogonalProjection.pdf
- Chapter 7. The Dual and Adjoint of a Linear Map — https://www.math.uwaterloo.ca/~snew/MATH245/Chap7DualAndAdjoint.pdf
- Chapter 8. Orthonormal Diagonalizations — https://www.math.uwaterloo.ca/~snew/MATH245/Chap8OrthonormalDiagonalization.pdf
- Chapter 9. Bilinear Forms — https://www.math.uwaterloo.ca/~snew/MATH245/Chap9BilinearForms.pdf
- Chapter 10. Quadratic Forms — https://www.math.uwaterloo.ca/~snew/MATH245/Chap10QuadraticForms.pdf
- Chapter 11. Tensor Algebras (Optional) — https://www.math.uwaterloo.ca/~snew/MATH245/Chap11TensorAlgebras.pdf
- Chapter 12. Jordan Canonical Form — https://www.math.uwaterloo.ca/~snew/MATH245/Chap12JordanForm.pdf
- Appendix: MATH 146 Notes (incomplete) — https://www.math.uwaterloo.ca/~snew/MATH245/math146notes.pdf
Sources
- Course catalogue ↗2026–2027
- course_website ↗Undated
- Public lecture-note archive by Stephen New. Topics are the chapter headings in the posted notes; this is not a current-term syllabus. Source term/year not established.