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An example of a 3 × 3 × 3 magic cube. In this example, no slice is a magic square. In this case, the cube is classed as a simple magic cube.. In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an n × n × n pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four ...
Synonym for (0,1)-matrix, binary matrix or Boolean matrix. Can be used to represent a k-adic relation. Markov matrix: A matrix of non-negative real numbers, such that the entries in each row sum to 1. Metzler matrix: A matrix whose off-diagonal entries are non-negative. Monomial matrix: A square matrix with exactly one non-zero entry in each ...
It is called an identity matrix because multiplication with it leaves a matrix unchanged: = = for any m-by-n matrix A. A nonzero scalar multiple of an identity matrix is called a scalar matrix. If the matrix entries come from a field, the scalar matrices form a group, under matrix multiplication, that is isomorphic to the multiplicative group ...
3D projections use the primary qualities of an object's basic shape to create a map of points, that are then connected to one another to create a visual element. The result is a graphic that contains conceptual properties to interpret the figure or image as not actually flat (2D), but rather, as a solid object (3D) being viewed on a 2D display.
The number n is called the order of the magic hypercube. This definition of "perfect" assumes that one of the older definitions for perfect magic cubes is used. The Universal Classification System for Hypercubes (John R. Hendricks) requires that for any dimension hypercube, all possible lines sum correctly for the hypercube to be considered ...
Catmull–Clark level-3 subdivision of a cube with the limit subdivision surface shown below. (Note that although it looks like the bi-cubic interpolation approaches a sphere, an actual sphere is quadric.) Visual difference between sphere (green) and Catmull-Clark subdivision surface (magenta) from a cube
Multiplying a matrix M by either or on either the left or the right will permute either the rows or columns of M by either π or π −1.The details are a bit tricky. To begin with, when we permute the entries of a vector (, …,) by some permutation π, we move the entry of the input vector into the () slot of the output vector.
Every Coxeter diagram has a corresponding Schläfli matrix (so named after Ludwig Schläfli), A, with matrix elements a i,j = a j,i = −2 cos(π /p i,j) where p i,j is the branch order between mirrors i and j; that is, π /p i,j is the dihedral angle between mirrors i and j. As a matrix of cosines, A is also called a Gramian matrix.