The Course in the Geometry of N Dimensions

PART 1 THE GEOMETRY OF n DIMENSIONS Introduction 1(4) Reality 5(1) Varieties 5(1) Intersections of varieties 5(3) Projection 8(1) Simple figures in n dimensions 9(2) Coordinate transformations 11(1) Helmert's transformation 12(3) Polar coordinates in n dimensions 15(3) Equation of a flat through given points 18(1) Angles 19(8) Reciprocity 27(1) Solid angles 28(1) Tangent (n---1)-flats 29(1) Reduction of a quadric to canonical form 29(5) The projection of an angle 34(1) Content 34(1) Content of a hypersphere 35(1) Content of a hyperellipsoid 36(1) Content of a hyperprism 36(1) Content of a parallelotope 36(1) Content of a hyperpyramid 37(1) Content of a simplex 38(9) PART 2 STATISTICAL APPLICATIONS Introduction 43(4) ``Student's'' t 47(1) The mean in rectangular variation 48(2) The correlation coefficient in bivariate normal variation 50(2) Wishart's distribution 52(3) Correlations as angles 55(3) Regression and multiple correlation 58(3) Canonical correlations 61(1) Component analysis 62(1) References 63