This course covers the basics of linear algebra and related topics, including vector algebra with its application to 3D geometry, matrix algebra with application to solving systems of linear equations, complex numbers/ vectors and discrete Fourier Transforms. Matrix topics will include linear transformations, eigenvalues and eigenvectors, similarity of matrices and applications of these. Concepts such as vector spaces, inner product spaces, and symmetric and orthogonal matrices are also introduced. Computer algorithms for performing various matrix operations and calculations and discrete Fourier Transforms will be explored.
This course offering is in progress. Please check back next term or subscribe to receive email updates.
Upon successful completion of this course, the student will be able to:
Solve systems of linear equations using common analytical and numerical matrix-based methods.
Perform matrix algebra calculations using +, -, ×, inversion, determinants and other common matrix operations.
Illustrate the use of vectors in 2- and 3-D space and the associated algebra of vectors, including the norm of a vector, vector arithmetic, and the dot/cross products with applications of vectors to lines and planes in 3-D space.
Use complex numbers, including complex vectors and matrices including quaternions.
Calculate the eigenvalues and eigenvectors of a matrix and apply to diagonalization of matrices.
Implement common computer algorithms for matrix calculations, such as decomposition, discrete Fourier Transforms and solving systems of equations.
Explain the function of Fourier transforms.
Explain general vector spaces and find the basis of a vector space along with its associated characteristics.
Determine transformations, mappings and projections between vector spaces.
Use matrices in an applied context, e.g. computer graphics, cryptography, principal component analysis, signal filter, etc..
Effective as of Fall 2018
MATH 7908 is offered as a part of the following programs:
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