marginprogram theorypoint 0D --> 4 1D --> 2 2D --> 10 3D --> 20 4D --> 40 vector 1D --> 2 * n° elements 2D --> 10 * n° elements 3D --> 20 * n° elements 4D --> 40 * n° elements example n° elements = 2 1D --> 4 --> point 0D 2D --> 20 --> point 3D 3D --> 40 --> point 4D 4D --> 80 to interpret vector of 2 elements to 1D is equal to speak of point 0D to interpret vector of 2 elements to 2D is equal to speak of point 3D to interpret vector of 2 elements to 3D is equal to speak of point 4D another example n° elements = 5 1D --> 10 --> point 2D 2D --> 50 3D --> 100 4D --> 200 to interpret vector of 5 elements to 1D is equal to speak of point 2D matrix 2D 2D --> 10 * area 3D --> 20 * area 4D --> 40 * area example n° elements = 4 2D --> 40 --> vector 3D of 2 elements --> point 4D 3D --> 80 --> vector 4D of 2 elements 4D --> 160 matrix 2D dimension 2x2 (matrix 2D) is equal vector 3D dimension 1x2=2x1 (vector) because numerical reference is the same numerical quantity (40) another example n° elements = 8 2D --> 80 --> vectors 4D of 2 elements 3D --> 160 4D --> 320 matrix 2D dimension 4x2=2x4 (matrix 2D) is equal vector 4D dimension 1x2=2x1 (vector) because numerical reference is the same numerical quantity (80) matrix 3D 3D --> 20 * volume 4D --> 40 * volume example n° elements = 8 3D --> 160 4D --> 320 matrix 3D dimension 2x2x2 (matrix 3D) is equal matrix 4D dimension 2x2 (matrix 2D) because numerical reference is the same numerical quantity (160) |