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, MATH 3300H
Prerequisite
MATH 2260 or MATH 2260E or MATH 2260H or MATH 2310H or MATH 2410 or MATH 2410H
Semester Course Offered
Offered fall, spring and summer
Grading System
A - F (Traditional)
Student learning Outcomes
Students will be able to solve systems of linear equations by means of Gaussian elimination.
Students will be able to calculate the inverse of a matrix.
Students be able to determine the projection operator onto a subspace.
Students will be able to determine the null space and range space of a linear transformation.
Students will be able to calculate the eigenvalues and eigenvectors of a matrix.
Students will be able to calculate the singular value decomposition of a matrix.
Students will gain experience in applying linear algebra to 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: null space, row space, 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 basic 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.
