Guide for Week 1
Math 408 Section A, January 7, 2013/h4>
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Reading Assignment:
Homework Assignment:
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Vocabulary List:
- Math 308 Review:
- m by n systems of linear equations
- Gaussian elimination
- echelon form
- dot product
- orthogonal vectors
- subspace
- basis and dimension
- internal representation of a subspace
- external representation of a subspace
- the 4 fundamental subspaces associated with a matrix
- rank and nullity
- properties of matrix multiplication
- manipulation of block structured matrices
- Gaussian elimination matrices
- Multivariate calculus review
- vector norm
- 1, 2, and infinity norms
- norm equivalence in finite dimensions
- continuity
- open, closed, bounded, and compact sets
- cluster points
- Weierstrass Extreme Value Theorem
- little-o notation
- differentiablity: gradients, hessians, and Jacobians.
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Key Concepts:
- Math 308 Review:
- Linear systems of equations
- Gaussian elimination as a method to attain echelon form
- Echelon form and the solution of a linear system
- Subspaces and their representations: internal and external
- Properties of the 4 fundamental subspaces associated with a matrix.
- Gaussian elimination as matrix multiplication,
and the LU factorization.
- Manipulation of block structured matrices
- Multivariable calculus review
- 1, 2, and infinity norms
- continuity and differentiablity
- compactness
- cluster points
- Weierstrass Extreme Value Theorem
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Skills to Master:
- Gaussian elimination, reduction to echelon form
- The use of Gaussian elimination matrices
and Householder transformations
- computing gradients, hessians, and Jacobians
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Quiz:
- This quiz is based on the vocabulary words and homework associated with
the Math 308 and multivariate calculus review material.
The quiz will consist of two parts
(each possibly multi-part). The first will be related to the vocabulary
words and the second will be computational.
A sample quiz can be found
here.