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Section
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Content
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Suggested Problems
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Section 5.5
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- Orthogonal set
- Orthonormal set
- Theorem 5.5.1
- Theorem 5.5.2 Coordinates computations for orthonormal bases
- Orthogonal matrix
- Properties of orthogonal matrices
- Theorem 5.5.7 Projection onto a subspace with an orthonormal basis
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1, 2, 3, 21
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Section 5.6
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- Theorem 5.6.1 Gram-Schmidt Orthogonalization Process
- Theorem 5.6.2 Gram-Schmidt QR Factorization
- Theorem 5.6.3 Least squares solution for matrix A with rank n via QR factorizaton
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1, 2, 3, 5, 8
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Section 6.1
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- Eigenvector
- Eignenvalue
- Characteristic polynomial
- Complex eigenvalues and eigenvectors of real matrices
- Compute eigenvalues and eigenvectors
- Product and sum of eigenvalues
- Eigenvalues of upper triangular matrix
- Eigenvalues of similar matrices
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1, 2, 11
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Section 6.3
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- Diagonalizable
- Theorem 6.3.2
- Arithmetic Multiplicity vs Geometric Multiplicity
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1, 2
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