• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Infinite Dimensional Vector Space
Post: #1

We are familiar with the properties of finite dimensional vector spaces over a field. Many of the results that are valid in finite dimensional vector spaces can very well be extended to infinite dimensional cases sometimes with slight modifications in definitions. But there are certain results that do not hold in infinite dimensional cases. Here we consolidate some of those results and present it in a readable form.

We present the whole work in three chapters. All those concepts in vector spaces and linear algebra which we require in the sequel are included in the first chapter. In section I of chapter II we discuss the fundamental concepts and properties of infinite dimensional vector spaces and in section II, the properties of the subspaces of infinite dimensional vector spaces are studied and will find that the chain conditions which hold for finite cases do not hold for infinite cases.

The linear transformation on infinite dimensional vector spaces and introduce the concept of infinite matrices. We will show that every linear transformation corresponds to a row finite matrix over the underlying field and vice versa and will prove that the set of all linear transformations of an infinite dimensional vector space in to another is isomorphic to the space of all row finite matrices over the underlying field. In section II we consider the conjugate space of an infinite dimensional vector space and define its dimension and cardinality and will show that the dimension of the conjugate space is greater than the original space. Finally we will show that the conjugate space of the conjugate space of an infinite dimensional vector space cannot be identified with the original space.
 « Next Oldest | Next Newest »

## Important Note..!

 Popular Searches: ppt for maths chapter vector space for gtu, vector space algebra, space aliens, a vector space approach to geometry, 3 dimensional password projects, vector space analysis, two leg space vector,

Message

Image Verification
 (case insensitive) Please enter the text within the image on the left in to the text box below. This process is used to prevent automated posts.

 Possibly Related Threads... Thread: Author Replies: Views: Last Post Space Vector Pulse Width Modulation (SVPWM) Scheme for Inverter Using MATLAB/SIMULINK project report helper 11 7,616 25-05-2016 01:38 AM Last Post: Guest A Neural-Network-Based Space-Vector PWM Controller for Voltage-Fed Inverter Inducti project report helper 1 1,272 07-09-2015 06:23 PM Last Post: hafsa_012 Space Time Adaptive Processing computer science crazy 4 4,247 04-03-2014 07:03 PM Last Post: Guest Space Vector Modulated Three-phase to Three-phase Matrix Converter with Input Power computer science technology 2 2,781 27-01-2013 11:46 AM Last Post: [email protected] Free Space Optics computer science crazy 1 1,870 25-02-2012 10:54 AM Last Post: seminar paper Speed Sensorless Vector Control of Induction Motors Based on Robust Adaptive Variable projectsofme 1 1,936 20-02-2012 04:53 PM Last Post: seminar paper optical space communication or Free-space optical communication(FSO) computer science crazy 3 5,106 15-02-2012 12:47 PM Last Post: seminar paper SPACE Based Solar power seminar class 0 1,903 21-03-2011 10:09 AM Last Post: seminar class SPACE FUTURE-THE GLOBAL SOLUTIONS FOR THE COMING ENERGY CRISIS seminar class 0 917 18-03-2011 11:29 AM Last Post: seminar class PEA Space Charge Measurement System project topics 1 1,941 27-11-2010 10:20 AM Last Post: projectsofme