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Matrix algebra and its use in least squares adjustments. Matrix calculus with Taylor Series linearization, eigenvalues and eigenvectors, quadratic forms and error ellipses.
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Upon successful completion, the student will be able to:
Carry out matrix operations.
Solve small systems of linear equations using determinants.
Apply matrix operations to the solution of geomatics problems such as adjusting a small level net.
Solve large systems of linear equations using Gauss elimination and Choleski decomposition.
Use Choleski decomposition to solve the normal equations found in geomatics problems such as the determination of the position of a point.
Find matrix inverses using Choleski decomposition.
Use matrix inverses in geomatics adjustments problems to help estimate the standard deviations of variables.
Carry out matrix differentiation.
Use matrix differentiation to linearize matrices of functions so that the positions of points can be estimated.
Illustrate the use of Lagrange multipliers in least squares adjustments.
Solve vector problems involving distance and direction in 2- and 3- space.
Apply some of the concepts of vectors in finding eigenvalues and eigenvectors.
Use eigenvalues and eigenvectors to find the magnitude and directions of the semi-major and semi-minor axes of error ellipses about points whose position has been determined through adjustment.
Effective as of Fall 2003
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