Machine generated contents note: 1.Introduction -- Perspective -- 1.1.A Recent Referee Speaks -- 1.2.The Original Motivation -- 1.3.The Essential Entities -- 1.4.Simple Examples and a Picture -- 1.5.Applications to-Date -- 1.6.Organization of this Book -- Commentary -- 1.7.Exercises -- 2.The Original Motivation: Operator Semigroups -- Perspective -- 2.1.Abstract Initial Value Problems -- 2.2.The Hille-Yosida-Phillips-Lumer Theorem -- 2.3.The Rellich-Kato-Nelson-Gustafson Theorem -- 2.4.The Multiplicative Perturbation Theorem -- 2.5.When are Positive Operator Products Positive? -- 2.6.Nonnegative Contraction Semigroups -- Commentary -- 2.7.Exercises -- 3.The Essentials of Antieigenvalue Theory -- Perspective -- 3.1.Convexity Properties of Norm Geometry -- 3.2.The Min-Max Theorem -- 3.3.The Euler Equation -- 3.4.Higher Antieigenvalues and Antieigenvectors -- 3.5.The Triangle Inequality -- 3.6.Extended Operator Trigonometry -- Commentary -- 3.7.Exercises --

Contents note continued: 4.Applications in Numerical Analysis -- Perspective -- 4.1.Gradient Descent: Kantorovich Bound is Trigonometric -- 4.2.Minimum Residual Ax = b Solvers -- 4.3.Richardson Relaxation Schemes (e.g. SOR) -- 4.4.Very Rich Trigonometry Underlies ADI -- 4.5.Domain Decomposition Multilevel Schemes -- 4.6.Preconditioning and Condition Numbers -- Commentary -- 4.7.Exercises -- 5.Applications in Wavelets, Control, Scattering -- Perspective -- 5.1.The Time Operator of Wavelets -- 5.2.Frame Operator Trigonometry -- 5.3.Wavelet Reconstruction is Trigonometric -- 5.4.New Basis Trigonometry -- 5.5.Trigonometry of Lyapunov Stability -- 5.6.Multiplicative Perturbation and Irreversibility -- Commentary -- 5.7.Exercises -- 6.The Trigonometry of Matrix Statistics -- Perspective -- 6.1.Statistical Efficiency -- 6.2.The Euler Equation versus the Inefficiency Equation -- 6.3.Canonical Correlations and Rayleigh Quotients -- 6.4.Other Statistics Inequalities --

Contents note continued: 6.5.Prediction Theory: Association Measures -- 6.6.Antieigenmatrices -- Commentary -- 6.7.Exercises -- 7.Quantum Trigonometry -- Perspective -- 7.1.Bell-Wigner-CHSH Inequalities -- 7.2.Trigonometric Quantum Spin Identities -- 7.3.Quantum Computing: Phase Issues -- 7.4.Penrose Twistors -- 7.5.Elementary Particles -- 7.6.Trigonometry of Quantum States -- Commentary -- 7.7.Exercises -- 8.Financial Instruments -- Perspective -- 8.1.Some Remarks on Mathematical Finance -- 8.2.Quantos: Currency Options -- 8.3.Multi-Asset Pricing: Spread Options -- 8.4.Portfolio Rebalancing -- 8.5.American Options with Random Volatility -- 8.6.Risk Measures for Incomplete Markets -- Commentary -- 8.7.Exercises -- 9.Other Directions -- Perspective -- 9.1.Operators -- 9.2.Angles -- 9.3.Optimization -- 9.4.Equalities -- 9.5.Geometry -- 9.6.Applications -- Commentary -- 9.7.Exercises -- Appendix A Linear Algebra -- A.1.Matrix Analysis -- A.2.Operator Theory --

Contents note continued: Appendix B Hints and Answers to Exercises.