by Jack Goldfeather (Carleton College)
This article originally appeared in:
Mathematics Magazine
April, 1996
Subject classification(s):
Analysis | Signal Analysis | NoiseApplicable Course(s):
3.8 Linear/Matrix Algebra | 4.17 Numerical AnalysisIf 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