Abstract
This chapter discusses the techniques for analyzing individual linear transformations on a finite-dimensional vector space. The methods involved in this analyzing technique first decompose a linear transformation A on a vector space V into linear transformations on certain subspaces of V in such a way that the behavior of A can be deduced from that of its component linear transformations. The chapter presents methods that are designed to obtain a matrix of a given linear transformation that is as close as possible to a diagonal matrix. If the minimal polynomial of a linear transformation is the product of linear polynomials over the scalar field at hand, then it is the sum of a diagonable and a nilpotent linear transformation. Other types of linear transformations on finite-dimensional inner-product space have the property that they commute with their adjoints. The adjoints include self-adjoint transformations, unitary transformations, and orthogonal transformations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
