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Using Quadratic Forms to Correct Orientation Errors in Tracking

by Jack Goldfeather (Carleton College)

This article originally appeared in:
Mathematics Magazine
April, 1996

Subject classification(s): Analysis | Signal Analysis | Noise
Applicable Course(s): 3.8 Linear/Matrix Algebra | 4.17 Numerical Analysis

If noise in data transmission produces a not quite orthogonal matrix that is known to be orthogonal, how does one find the "nearest" orthogonal matrix?  This capsule recasts the problem as one of maximizing a quadratic form on the four-dimensional unit sphere, and sketches a solution.

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Capsule Course Topic(s):
Linear Algebra | Application: Signal & Image Processing
Linear Algebra | Eigenvalues and Eigenvectors
Linear Algebra | Matrix Factorizations
Linear Algebra | Quadratic Forms
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