This 54 page Math 2051 Final Exam preparation guide includes examples and all theorems, lemmas, and corollaries dealing with the topics after the second midterm, and does not cover the entire course:
Chapter 1 Material
- Orthogonality
- The “Best Solution” to a System of Equations
- Projection Matrices and Least Squares Approximation
- Data Fitting
Chapter 2 Material
- The Gram-Schmidt Algorithm
- QR-Factorization
- Orthogonal Matrices
- Least Squares Revisited
Chapter 3 Material
- Eigenvalues and Eigenvectors
- Similarity and Diagonalization
- Complex Numbers and Vectors
- Complex Matrices
- Unitary Diagonalization
- Real Symmetric Matrices are Orthogonally Diagonalizable
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