#### 4.1.7 ND Transformation matrices

In the context of N-dimensional space (N > 3) some objects incorporate (N+1)x(N+1) real matrices for homogeneous object transformations. These matrices act by multiplication on the right of vectors. Thus, if p is an (N+1)-element row vector representing homogeneous coordinates of a point in the OOGL object, and A (N+1)x(N+1) is the matrix, then the transformed point is p' = p A.

Note that (unlike for the 4x4 transformation matrices, see Transformation matrices) the homogeneous component is located at index zero, so the translation components for Euclidean transformations appear in the zero-th row (first (N+1) elements). A's first column (at column index zero) is typically 1, 0, ..., 0.