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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 Matrices      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 Eigenvalues      Complex eigenvalues      Diagonalization of matrices      Spectral theorem for symmetric (*hermitian) matrices      *Quadratic forms      Positive definite matrices      *Nonnegative matrices Applications      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) MATLAB use      In assigned homework through the semester TEXT Text(s) typically used in this course.