ABSTRACT
In this chapter, the authors show how to compute the Jordan canonical form and how to determine the associated basis of the vector space. From several points of view – including computations – the ideal representation of a linear transformation is a diagonal matrix, but this is not always possible. It is possible if and only if there is a basis of eigenvectors. The central ideas in the construction of the Jordan canonical form are generalized eigenvectors and chains of generalized eigenvectors. Jordan is best remembered today among analysts and topologists for his proof that a simply closed curve divides a plane into exactly two regions, now called the Jordan Curve Theorem. He also originated the concept of functions of bounded variation and is known especially for his definition of the length of a curve.
