Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering
If PA(χ) denotes the probability that the maximum condition number along a great circle passing through a matrix A in the unit sphere in the space of 2 × 2 matrices is less than χ, then PA(χ) always attains its maximum at the normalized identity matrix. This result is the first nontrivial case of a linear algebra version of a conjecture formulated in Shub and Smale (M. Shub and S. Smale, Theoretical Computer Science 113 (1994) 141-164) for homotopies of systems of homogeneous equations. The Hopf fibration is used to relate the probability PA(χ) to the area of an 'ellipse' on a sphere in ℝ3. © 1999 Elsevier Science Inc. All rights reserved.
Michael Ray, Yves C. Martin
Proceedings of SPIE - The International Society for Optical Engineering
A. Grill, B.S. Meyerson, et al.
Proceedings of SPIE 1989
James Lee Hafner
Journal of Number Theory
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Journal of Global Optimization