My Math Forum  

Go Back   My Math Forum > Math Forums > Math Events

Math Events Math Events, Competitions, Meetups - Local, Regional, State, National, International


Reply
 
LinkBack Thread Tools Display Modes
January 10th, 2014, 08:55 AM   #1
Member
 
Joined: Jan 2013

Posts: 96
Thanks: 0

Matrices

Find two 2x2 matrices with real entries A, B such that . (I need just an example.)
yo79 is offline  
 
January 10th, 2014, 10:32 PM   #2
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,182
Thanks: 181

Re: Matrices

Quote:
Originally Posted by yo79
Find two 2x2 matrices with real entries A, B such that . (I need just an example.)
Nice question!

Well i played around with it for a while till i realized we could work with rows as one way to get an answer.



agentredlum is offline  
January 11th, 2014, 09:10 AM   #3
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Matrices

Nice question with a nice solution!
mathbalarka is offline  
January 11th, 2014, 11:22 AM   #4
Member
 
Joined: Jan 2013

Posts: 96
Thanks: 0

Re: Matrices

Thank you!
yo79 is offline  
January 12th, 2014, 04:06 AM   #5
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,182
Thanks: 181

Re: Matrices

You're welcome.

Just in case you haven't noticed , we now have an easy solution to an infinite amount of problems of this form.

For

IF



THEN a solution will be





We can also transpose both A , B and get another family of solutions. Then we would be working with columns.

An interesting question to ask is 'what if ?'

A place to start could be ,

Find a 22 matrix A such that



Can it be found ?

agentredlum is offline  
January 12th, 2014, 09:12 AM   #6
Member
 
Joined: Jan 2013

Posts: 96
Thanks: 0

Re: Matrices

Of course not, if A has real entries ( det(A)^2=-1)!
yo79 is offline  
January 12th, 2014, 09:39 AM   #7
Global Moderator
 
CRGreathouse's Avatar
 
Joined: Nov 2006
From: UTC -5

Posts: 16,046
Thanks: 932

Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms
Re: Matrices

Quote:
Originally Posted by agentredlum
Find a 22 matrix A such that



Can it be found ?
Not in the real numbers. There is a unique complex solution up to the order of the variables.
CRGreathouse is offline  
January 12th, 2014, 09:42 AM   #8
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,182
Thanks: 181

Re: Matrices

Can we find A with complex entries?

agentredlum is offline  
January 12th, 2014, 12:06 PM   #9
Math Team
 
mathbalarka's Avatar
 
Joined: Mar 2012
From: India, West Bengal

Posts: 3,871
Thanks: 86

Math Focus: Number Theory
Re: Matrices

Quote:
Originally Posted by CRGreathouse
Not in the real numbers.
Indeed.
mathbalarka is offline  
January 13th, 2014, 03:44 AM   #10
Math Team
 
agentredlum's Avatar
 
Joined: Jul 2011
From: North America, 42nd parallel

Posts: 3,182
Thanks: 181

Re: Matrices

Find 4 distinct matrices A such that



agentredlum is offline  
Reply

  My Math Forum > Math Forums > Math Events

Tags
matrices



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Matrices Ter Linear Algebra 1 January 18th, 2013 05:51 AM
Help with matrices mario Algebra 3 March 28th, 2009 08:09 AM
Matrices FancyChancey Algebra 2 October 21st, 2008 09:48 AM
Matrices help aruwin Abstract Algebra 0 January 1st, 1970 12:00 AM





Copyright © 2017 My Math Forum. All rights reserved.