Tensor Trigonometry

Description:

This initiative math monograph in its original Russian edition (2004) was being created by the author sequentially and step by step in period 1998-2003 in rare free time from his labor and life activity and was finished with its large Appendix by the end of 2003, what is mapped on the author's personal web-site http://ninulas.narod.ru with English main page. Though principal results of its preliminary fundamental Part I was gotten by him else in 1981. The initial impulse consisted in solving by him in the middle 1980 year a problem from the Analytical Geometry, namely, to obtain exact non-rational and limit formulas for the vector-perpendicular falling from a given point onto a given plane in the Euclidean space through known elements of matrix and vector parameters in this task (in particular, as a normal and in general non rational (how usually) solution of a linear algebraic equation). The well-known article of Russian Academician A.N. Tikhonov of 1965 about equation’s normal solution by the regularization method with the use of a small parameter served to the author as the starting point for creating the preliminary Part I of his future book, what was logically developed by him further many later up to the entire contents of the book Tensor Trigonometry.

subjects: Mathematics,  Geometry,  Algebra,  General inequality for all average values,  Algebraic equations (theory and solution),  Equation roots reality (positivity) criterion,  Linear Algebra,  Matrix Theory,  Characteristic coefficients of a matrix,  Singularity parameters of a matrix (interrelation and inequalities),  Pseudoinverse matrices (exact and limit formulas),  Singular matrices,  Null-prime matrix,  Null-normal matrix,  Lineor,  Planar,  All quadratic norms of matrix objects,  Group Theory,  Quasi-Euclidean space of index q or 1,  Pseudo-Euclidean space of index q or 1,  Plane Trigonometry,  Pseudoplane Trigonometry,  Tensor Calculus,  Tensor Trigonometry,  Eigenprojectors,  Eigenreflectors,  Orthogonal,  Oblique,  Affine,  Tensor angle and its functions,  Spherical,  Hyperbolic,  Orthospherical,  Matrix trigonometric spectrum,  Cosine and Sine relations and inequalities for matrix objects,  Tensor of motion (or rotation),  Principal motion (or rotation),  Orthospherical motion (or rotation),  Polar decompositions of a motion tensor,  QR-decomposition of a lineor,  Multi-dimensional Geometry,  Non-Euclidean Geometries,  Geometries trigonometric models,  Motions trigonometric models,  Noncommutative Pythagorean Theorem,  Angular defect (nature),  Angular excess (nature),  Oriented hyperspheroid,  Minkowski hyperboloids,  Beltrami pseudosphere,  Mathematical Physics,  Relativity,  Minkowski space-time,  Geometry of world lines,  Kinematics,  Dynamics,  Thomas precession,  Relativistic effects (trigonometric interpretation),  Relativistic Laws of Conservation (their conditions),  Mathematical Principle of Relativity,  Ninul

Places: Moscow