Section
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Content
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Suggested Problems
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Section 4.1
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- Examples
- Properties
- L(0V) = 0W
- L(-x) = -L(x)
- Linear combinations
- Kernel of L
- Image of a Subspace under L
- Range of L
- Theorem 4.1.1
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1, 4, 5, 6, 7, 9, 11, 17, 19
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Section 4.2
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- Theorem 4.2.1 Matrix representation of Linear Transformation from Rn to Rm
- Theorem 4.2.2 Matrix representation of Linear Transformation from V to W
- Theorem 4.3.3 Construction of Matrix A for case of V = Rn and W = Rm in Theorem 4.2.2
- Corollary Above construction via row equivalent transformation of an augmented matrix
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1, 2, 3, 4, 6, 14, 18
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Section 4.3
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- Linear Operator
- Theorem 4.3.1
- Similarity
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1, 3, 4, 5
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Section 5.1
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- Scalar product of vectors in Rn
- Length of a vector in in Rn
- Distance between two vectors in in Rn
- Angle between two vectors in Rn
- Cauchy-Schwarz Inequality
- Definition of orthogonality for vectors in Rn
- Projections
- Vector projection of x onto y
- Scalar rojection of x onto y
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1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13,
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Section 5.2
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- Orthogonal subspaces
- Orthogonal complement of a subspace
- Theorem 5.2.1 Fundamental Subspaces Theorem
- Direct sum of subspaces
- Theorem 5.2.3
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1, 2, 4, 5,
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Section 5.3
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- Least Square Problem for Ax = b
- Theorem 5.3.1
- Normal Equations for Least Squares Problem
- Theorem 5.3.2 Least squares soluton for matrix A with rank n
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1a, 1b, 2
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