MATH 400 (Vectors and Matrices)
| DESCRIPTION |
The course presents the essentials of matrix theory and
linear algebra
needed in the management,
social and biological sciences, and it provides mathematical background
for courses in
multivariate statistics, biostatistics, and econometrics.
(NOTE: The course is not open to students in the CMPS or
Engineering
Colleges.
Credit will only be given for one of Math 240, 400, 461.) |
| PREREQUISITES |
One year of college calculus, MATH 140/141 or
MATH 220/221. |
| TOPICS |
Systems of Linear Equations
Echelon forms
Existence and Uniqueness of solutions
Applications: Networks, production planning
Vector and Matrix Equations
Vectors in Rn
Matrix notation for systems of equations
Linear independence
Introduction to linear transformations
Applications: Nutrition and population
movement
Matrix Algebra
Matrix multiplication and inverses
The invertible matrix theorem
Application: Leontief economic models
Vector Spaces
Vector spaces and subspaces
Linear independence and bases
Dimension and rank
The Rank Theorem for m x n matrices
Application: Markov Chains
Orthogonality in Rn
Scalar product
Orthogonality and projections
Best approximation and abstract least squares
Application: Linear models in statistics
Eigenvalue Problems
Eigenvalues
Brief Introduction to determinants the
characteristic
equation
Diagonalization of matrices
Application: Age-specific population growth
Application: Difference equations |
| TEXT |
Text(s)
typically used in this course. |
|
