Overview of Week 8
Math 308M, November 11, 2013
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Reading Assignment:
- Read Section 3.6 for Monday Oct 28.
- Read Section 3.7 for Friday Nov 1.
- Read Section 3.8 for Wednesday Nov 13.
- Read Section 3.9 for Friday Nov 15.
- Read Section 4.1 for Wednesday Nov. 20
- Read Section 4.2 for Friday Nov 22
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Homework Assignment:
- Due Nov 4
- Sec. 3.5: 2, 4, 6, 8, 12, 15, 18, 22, 24, 26, 32, 34, 36, 40
- Due Nov 13
- Sec. 3.6: 1, 8, 9, 13, 18, 22, 28
- Due Nov 18
- Sec. 3.7: 1, 2(a, b), 3, 9, 10, 11, 18, 19, 22, 27, 28, 29, 35, 38, 46(a, b, c)
- Due Nov 25
- Sec. 3.8: 3, 7, 11
- Sec. 3.9: 1, 12
- Sec. 4.1: 3, 4, 13, 19
- Sec. 4.2: 9, 14, 15, 17, 25, 26, 27, 28
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Vocabulary List:
- Section 3.6:
- orthogonal vectors, set, and bases
- orthonormal basis
- coordinates in a basis
- Gram-Schmidt orthogonalization process
- the Cauchy-Schwartz inequality
- the triangle inequality
- Section 3.7:
- linear tranformation
- the identity, dialations, and contractions
- the matrix of a linear tranformation
- the null space and range of a linear transformation
- rank and nullity
- the rank plus nullity theorem
- orthogonal linear transformations
- rotations and reflections
- Sections 3.8 and 3.9
- The least-squares optimization problem
- the least-squares residual vector
- the least-squares solution
- consistency of the least-squares problem
- the normal equations
- the gradient of the least-squares objective
- full rank
- rank deficient matrices
- existence and uniqueness criteria for least-squares problems
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Key Concepts:
- Section 3.6:
- orthogonality and orthogonal bases
- the Gram-Schmidt orthogonalization process
- Section 3.7:
- the matrix of a linear tranformation
- orthogonal linear transformations
- Sections 3.8 and 3.9
- least-squares optimization
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Skills to Master:
- computing and orthonormal spanning set and an orthonormal basis
- computing the matrix associated with a linear transformation
- computing a solution to a least-squares problem
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Quiz:
Friday, November 15.
- The quiz is based on the vocabulary words and homework for Section 3.6 of the book.