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MATH 461 (Linear Algebra for Scientists and Engineers)

DESCRIPTION The course provides an introduction to linear algebra and matrix theory.  It is intended primarily for engineering students.  This course cannot be used toward the upper level math requirements for MATH/STAT majors.  Credit will be granted for only one of the following: MATH 240, MATH 400, MATH 461.
PREREQUISITES MATH 141 and one MATH/STAT course for which MATH 141 is a prerequisite.
TOPICS Systems of Linear Equations
     Gaussian elimination
     Echelon forms
     Existence and uniqueness of solutions
     Homogeneous systems
     Addition, scalar multiplication, multiplication of matrices
     Elementary matrices and inversion
     LU decomposition
     Systems of linear equations as matrix equations
     *Partitioned matrices
     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
     Complex eigenvalues
     Diagonalization of matrices
     Spectral theorem for symmetric (*hermitian) matrices
     *Quadratic forms
     Positive definite matrices
     *Nonnegative matrices
     Including several of the following:
     *Liontief Input-Output Model
     *Markov Chains
     *Computer Graphics
     *Least squares data fitting
     *Fourier Series
     *Systems of Differential Equations
     *Difference Equations
     *Max-Min Theory for functions of several variables (Hessian Matrix)
     In assigned homework through the semester

TEXT Text(s) typically used in this course.