Abstract
The chapter begins with notion of the Plucker coordinates of a subspace in a vector space. Then the Plucker relations are derived, and the Grassmann varieties are described. Then an exterior product of vectors is defined, and the connection between the exterior product and Plucker coordinates is explained: the Plucker relations give necessary and sufficient conditions for an m−vector to be represented as an exterior product of m vectors of the initial vector space. The properties of an exterior product are investigated in greater detail; the notion of exterior algebra is introduced and discussed. Finally, several applications of the obtained theoretical results are considered, for instance, Laplace’s formula for determinant of a square matrix and the Cauchy–Binet formula for the determinant of the matrix product are proved using the exterior product.
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.
