Matrices

Abstract

Matrices play an important role in representing rotation transforms, and because of their importance, this chapter assumes that the reader is meeting them for the first time. The chapter begins by showing how matrices simplify the solution to simultaneous equations using the idea of the inverse matrix. The reader is then formally introduced to computing the transpose, the identity matrix, adding, subtracting and multiplying matrices, the inverse, the determinant, orthogonal and diagonal matrices. The second half of the chapter introduces more advanced topics such as the trace, symmetric and antisymmetric matrices, the characteristic equation, eigenvectors and eigenvalues. The latter are eventually used to extract the axis of rotation from a rotation matrix and the angle of rotation. The chapter concludes with a summary and a list of the matrix operations covered.