An operator trigonometry developed chie_y by this author during the past 40 years has interesting applications to statistics, and provides new geometrical understandings of statistical efficiency, canonical correlations, and other statistical bounds and inequalities.
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References
Gustafson, K.: Antieigenvalue Inequalities in Operator Theory, Inequalities III (O. Shisha, ed.), Academic, 115 119 (1972).
Gustafson, K.: On Geometry of Statistical E ciency. (1999, preprint).
Gustafson, K.: An Unconventional Linear Algebra: Operator Trigonometry, in Un-conventional Models of Computation (I. Antoniou, C. Calude, M. Dinneen, eds.), Springer, 48 67 (2001).
Gustafson, K.: An Extended Operator Trigonometry. LAA 319, 117-135 (2000).
Gustafson, K.: Operator Trigonometry of Statistics and Econometrics. LAA. 354, 151-158 (2004).
Gustafson, K.: The Geometry of Statistical E ciency, Research Letters Inf. Math. Sci. 8, 105-121 (2005).
Gustafson, K.: The Trigonometry of Matrix Statistics, International Statistical Re-view. 74, 187-202 (2006).
Gustafson, K.: The Geometry of Statistical E ciency and Matrix Statistics, J. of Applied Math. and Decision Sciences, to appear. (2007a).
Gustafson, K.: Lectures on Computational Fluid Dynamics, Mathematical Physics, and Linear Algebra, World Scienti c, Singapore. (1997).
Gustafson, K. and Rao, D.K.M.: Numerical Range, Springer. (1997).
Gustafson, K: Noncommutative Trigonometry, Operator Theory: Advances and Ap-plications. 1967, 127-155 (2006).
Gustafson, K: Noncommutative Trigonometry and Quantum Mechanics, in Advances in Deterministic and Stochastic Analysis (N. Chuong, P. Ciarlet, P. Lax, D. Mum-ford, D. Phong, eds.), World Scienti c, 341 360 (2007b).
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Gustafson, K. (2008). The Operator Trigonometry in Statistics. In: Functional and Operatorial Statistics. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2062-1_29
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DOI: https://doi.org/10.1007/978-3-7908-2062-1_29
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