MATH 461 Linear Algebra for Scientists and Engineers
Exam Schedule
- First Exam:
- Friday, 27 February 2004.
- Second Exam:
- Wednesday, 31 March 2004.
- Third Exam:
- Friday, 30 April 2004.
- Final Exam:
- Tuesday, 18 May 2004, 8 - 10.
Grading Policy
Grades will be based on three hour exams counting
100 points each, homework and quizzes worth 100 points, MATLAB assignments
worth 100 points, and a final examination that is worth 200 points.
Class Schedule
The class meets according to the following schedule:
- Monday, Wednesday, and Friday, 12:00-1:00
- Math Building 0307.
Topics
- TOPICS
- Systems of Linear Equations
- Gaussian elimination
- Echelon forms
- Existence and uniqueness of solutions
- Homogeneous systems
- Matrices
- Addition, scalar multiplication, multiplication of matrices
- Elementary matrices and inversion
- LU decomposition
- Systems of linear equations as matrix equations
- Determinants and their properties
- Cramer's rule
- Vector Spaces
- Subspaces and spanning sets
- Linear independence
- Basis and dimension
- Row and column spaces of a matrix
- Rank of a matrix
- Null space of a matrix
- Linear Transformations
- Kernel and range
- Matrix representation
- Change of basis and similarity of matrices
- Scalar Products and Orthogonality
- Cauchy-Schwarz and triangle inequalities
- Length and angles
- Pythagorean theorem
- Orthonormal sets
- Orthogonal complements of the null space and column space
- Orthogonal projection
- Least squares problems
- Orthogonal matrices
- Gram-Schmidt process and QR factorization
- Eigenvalues
- Complex eigenvalues
- Diagonalization of matrices
- Spectral theorem for symmetric (*hermitian) matrices
- Positive definite matrices
- Singular Value Decomposition
Topics in Strang
We wil cover Chapters 1-6 of Strang's book, and topics from Ch. 7 (Linear
Transformations), Ch. 8(Applications), Ch. 9 (Numerical Linear Algebra), and
Ch. 10 (complex Vectors and Complex Matrices) if there is time.