Welcome! You have found the homepage of the Spring 2025 manifestation of Math 781.
Quizzes and problem sets are distributed through gradescope.
| Timeframe | Topic | Resources |
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| Week 0 | Welcome! | |
| Week 1 | Matrices and Vectors |
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| Adjectives ⟵ complete at home! |
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| Matrix-Vector Products |
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| Week 2 | Digraphs |
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| Vector Geometry |
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| Matrix Multiplication ⟵ covered in week 3 |
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| Week 3 | Row Echelon Forms |
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| Linear Systems |
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| Week 4 | Gauss-Jordan Elimination |
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| Week 5 | Nonsingular Matrices |
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| EA=R Factorizations |
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| PA=LU Factorizations |
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| Week 6 | Eigenvalues |
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| Null Spaces |
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| Week 7 | Column Spaces |
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| The Four Fundamental Subspaces |
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| Linear Independence |
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| Week 8 | Bases |
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| Dimension |
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| Orthogonality |
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| Week 9 | Projections |
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| Least Squares |
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| Week 10 | A=QR Factorizations |
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| The Gram-Schmidt Algorithm |
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| Determinants I |
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| Week 11 | Determinants II |
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| Complex Numbers |
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| Week 12 | Polynomial Algebra |
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| The Characteristic Polynomial |
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| Week 13 | Diagonalization |
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| The Spectral Theorem |
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| Week 14 | Definiteness |
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| Singular Value Decomposition |
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