Abstract
Conventional computational linear algebra is chiefly concerned with the linear solver problem: Ax = b. Many fine algorithms for many situations have been found and these are widely utilized in scientific computing. The theory and practice of general linear solvers is intimately linked to the eigenvalues and eigenvectors of the matrix A. Here I will present a theory of antieigenvalues and antieigenvectors for matrices or operators A and show how that theory is also intimately linked to computational linear algebra. I will also present new applications of this theory, which I call operator trigonometry, to Statistics and Quantum Mechanics. Also I will give some hitherto unpublished insights into the operator trigonometry, its origins, meaning, and future potential. Finally, I will present a fundamental new view of sin φ(A).
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Gustafson, K. (2001). An Unconventional Computational Linear Algebra: Operator Trigonometry. In: Antoniou, I., Calude, C.S., Dinneen, M.J. (eds) Unconventional Models of Computation, UMC’2K. Discrete Mathematics and Theoretical Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-0313-4_4
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DOI: https://doi.org/10.1007/978-1-4471-0313-4_4
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