My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum

LinkBack Thread Tools Display Modes
August 12th, 2015, 01:47 PM   #1
Joined: Mar 2015
From: Brasil

Posts: 90
Thanks: 4

Vector Spaces

Attached Images
File Type: jpg Prova que é um Vspaço Vetotial....jpg (21.4 KB, 8 views)
Luiz is offline  
August 12th, 2015, 02:05 PM   #2
Global Moderator
greg1313's Avatar
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,898
Thanks: 1093

Math Focus: Elementary mathematics and beyond
Can a translation be provided?
greg1313 is offline  
August 13th, 2015, 08:39 AM   #3
Math Team
Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 895

I don't pretend to speak English, but I think it says:

For the set of all real valued functions, defined on set S, we define addition by [f+ g](x)= f(x)+ g(x) for all x and y in S, and scalar multiplication by (af)(x)= af(x) for all x in S and a any real number.

Prove that this set, with these operations, satisfies all the requirements of the definition of "Vector Space".

Those requirements are:
The set is closed under addition: if f and g are such functions, the f+ g is also a function from S to real numbers.
The set is close under multiplication: if f is such a function and a is a real number, then af is a function from S to real numbers.
One also needs to show that addition is commutative and associative, scalar multiplication is associative in the sense that a(bf)= (ab)f, that there exist an additive identitity, and each function has an additive inverse.

Those follow almost immediately from the fact that, for any x, f(x) is a real number and those properties are true of real numbers.
Country Boy is offline  

  My Math Forum > College Math Forum > Linear Algebra

spaces, vector

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Vector and spaces Notbright Linear Algebra 1 May 29th, 2015 05:45 AM
Vector spaces bamby Linear Algebra 5 January 30th, 2014 02:39 PM
Vector Spaces anyone? alphaknight61 Linear Algebra 1 November 26th, 2012 05:54 AM
vector spaces remeday86 Linear Algebra 1 July 10th, 2010 05:20 AM
vector spaces al1850 Linear Algebra 1 March 20th, 2008 10:50 AM

Copyright © 2019 My Math Forum. All rights reserved.