Course Description
Linear algebra from an applied and computational viewpoint. Linear equations, vector spaces, linear transformations; linear independence, basis, dimension; orthogonality, projections, and least squares solutions; eigenvalues, eigenvectors, singular value decomposition. Applications to science and engineering.
Athena Title
Applied Linear Algebra
Equivalent Courses
Not open to students with credit in MATH 3000, MATH 3300E
Prerequisite
MATH 2260 or MATH 2260E or MATH 2310H or MATH 2410 or MATH 2410H
Semester Course Offered
Offered fall, spring and summer
Grading System
A - F (Traditional)
Course Objectives
This is a first course in linear algebra which is less theoretical and more oriented towards applications than Introduction to Linear Algebra. Students should understand the concepts of vector spaces, bases, linear transformation, and matrix algebras. Students should be able to do the following: (1) Solve systems of linear equations by means of Gaussian elimination (2) Calculate the inverse of a matrix (3) Determine the projection operator onto a subspace (4) Determine the null space and range space of a linear transformation (5) Calculate the eigenvalues and eigenvectors of a matrix (6) Calculate the singular value decomposition of a matrix (7) Use linear algebra in problems of science and engineering
Topical Outline
1. Vector algebra. Dot products. Matrices. 2. Solving linear equations using elimination. 3. Matrix algebra: product, inverse, and transpose. 4. Subspaces: nullspace, rowspace, column space of a matrix. 5. Linear independence, basis, and dimension, orthogonal complement. 6. Orthogonality. Projections and least-squares approximation. Gram-Schmidt process. Change of basis formula. 7. Determinants. Cramer's rule. 8. Eigenvalues and eigenvectors, diagonalizability. Singular value decomposition. 9. Applications to science and engineering, including topics such as networks, Markov processes, linear programming, statistics, computer graphics.
Syllabus