BSNS102 Study Guide - Final Guide: Orthogonal Matrix, Rotation Matrix, Round-Off Error

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

Document Summary

Let"s consider this last point in more detail. If we take any nine numbers at random and create a. 3 3 matrix, it is very unlikely that these six constraints will be satisfied. Thus, the nine numbers will not form a valid rotation matrix. In other words, matrices can be ill-formed, at least for pur- poses of representing an orientation. Ill-formed matrices can be a problem because they can cause numerical exceptions and other unexpected behavior. There are several ways: n first, we may have a matrix that contains scale, skew, or reflection. There really isn"t a clear definition for this. Any non-orthogonal matrix is not a well-defined rotation matrix. (see section 9. 3 for a complete discussion on orthogonal matrices. ) Reflection matrices, which are orthogonal, are not valid rotation matrices either. n second, we may just get bad data from an external source.