Abstract
This chapter focuses on some preliminary mathematical concepts. A normed space is a vector space on which a real-valued transformation is defined such that it assigns to each element. The procedure by which an orthonormal basis is obtained is called the Gram–Schmidt procedure. The determinant of the Gram matrix is referred to as the Gram determinant. In a normed space, every convergent sequence is a Cauchy sequence. If a sequence converges in a normed space, its limit is unique. A complete normed space is called a Banach space. A complete vector space X together with an inner product defined on X × X is called a Hilbert space. In a normed space, any finite-dimensional subspace is complete. Every subset of a countable set is either a finite set or a countable set, and the set of all finite sequences from a countable set is countable.
Sign-in/Register to access full text options 
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 callMore From: Mathematics for Stability and Optimization of Economic Systems
Disclaimer: 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.
