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# MATH 3511 - Matrix Methods for Geomatics

## Mathematics Part-time Studies Course

### School of Computing and Academic Studies

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# Course Details

Matrix algebra and its use in least squares adjustments. Matrix calculus with Taylor Series linearization, eigenvalues and eigenvectors, quadratic forms and error ellipses.

## Credits

4.0

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# Learning Outcomes

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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