Matrix inversion
After describing the preconditions for the existence of an inverse and its definition, two procedures to determine the inverse of a matrix, the Gauß-Jordan-Algorithm and the Adjugate Formula, are introduced and clarified by examples.
Transformations
In this article general transformations used in the context of robotics and the underlying mathematics are described. The easiest type of transformation is translation, followed by rotation, scaling and shearing. To be able to apply all types of transformations by matrix multiplication, homogeneous coordinates are introduced. Based on the four basic transformations, combinations of different transformations are possible, that change for example the orientation and the position of an object.