More on Matrices

This chapter introduces homogeneous vectors and 4 × 4 matrices, and shows how they can be used to perform affine transformations in 3D. It discusses perspective projection and shows how to do it with a 4 × 4 matrix. Orthogonal matrices are interesting to us primarily because their inverse is trivial to compute. The determinant of a matrix has an interesting geometric interpretation. In 2D, the determinant is equal to the signed area of the parallelogram or skew box that has the basis vectors as two sides. The determinant of the matrix can also be used to help classify the type of transformation represented by a matrix. If the determinant of a matrix is zero, then the matrix contains a projection. Orthogonal matrices are interesting to us primarily because their inverse is trivial to compute.