Math 5250: Graduate Linear Algebra

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Week 12 — Bilinear Forms
Signature and definiteness

Math 5250: Graduate Linear Algebra
Math 5250 Schedule
Week 1 — Review
Weeks 2–3 — Abstract Vector Spaces
Week 4 — Eigenvalues and Eigenvectors
Weeks 5–6 — Inner Product Spaces
Weeks 7–8 — Matrix Decompositions
Week 9 — Norms
- Vector space norms and equivalence of norms
- Matrix and operator norms
Weeks 10–11 — Dual Spaces
Week 12 — Bilinear Forms
Weeks 13–14 — Multilinear Algebra

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Week 12 — Signature and Definiteness

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Notes on positive-definiteness, Sylvester’s law of inertia, and the signature of a symmetric bilinear form.