BSNS102 Study Guide - Final Guide: Invertible Matrix, Orthogonalization, Unit Vector

• School: University of Otago
• Department: Business Studies
• Course: BSNS102
• Professor: Drew Stelljes

Document Summary

The inverse of a matrix is useful geometrically because it allows us to compute the reverse or. Opposite of a transformation a transformation that undoes another transformation if they are performed in sequence. So, if we take a vector, transform it by a matrix m, and then transform it by the inverse m 1 of m, then we will get the original vector back. In this section, we will investigate a special class of square matrices known as orthogonal matrices. A square matrix m is orthogonal if and only if the product of the matrix and its transpose is the identity matrix: Recall from section 9. 2 that, by definition, a matrix times its inverse is the identity matrix: Thus, if a matrix is orthogonal, the transpose and the inverse are equal: This is extremely powerful information, since the inverse of a matrix is often needed, and orthogo- nal matrices arise so frequently in practice in 3d graphics.