Two Plus Two Newer Archives Linear algebra, matrices, and you
 FAQ Members List Calendar Search Today's Posts Mark Forums Read

#1
04-21-2006, 03:21 PM
 TBag Senior Member Join Date: Sep 2004 Location: In a raccoon suit Posts: 1,083
Linear algebra, matrices, and you

So yes, here is a math problem I'm rather curious about. In this situation, I'm guessing that A is just an identity matrix of n x n, would that be correct? If so, how would one go about proving it?

Also, for the true or false questions I got
1 true
2 false
3 I'm pretty sure this one is true, because if C = A^-1, and B = C^-1, therefore A=B, but I'm not sure I'll work one out and then edit my answer in
4 True

edit - I did number 3 with the matrix
1 2
3 4
And it proved the statement true. Is there any instance where it wouldn't?
#2
04-21-2006, 03:49 PM
 brandofo Senior Member Join Date: Nov 2005 Posts: 816
Re: Linear algebra, matrices, and you

[ QUOTE ]
So yes, here is a math problem that I need to finish by Monday. Please do it for me.

[/ QUOTE ]
FYP
#3
04-21-2006, 03:55 PM
 TBag Senior Member Join Date: Sep 2004 Location: In a raccoon suit Posts: 1,083
Re: Linear algebra, matrices, and you

Dude, it's a bonus problem.
#4
04-21-2006, 04:08 PM
 thedustbustr Senior Member Join Date: Sep 2005 Posts: 8,556
Re: Linear algebra, matrices, and you

[ QUOTE ]
I'm guessing that A is just an identity matrix of n x n

[/ QUOTE ]
No need to guess, this is given. rereading the question would probably be a good wy to get started.
#5
04-21-2006, 04:25 PM
 TBag Senior Member Join Date: Sep 2004 Location: In a raccoon suit Posts: 1,083
Re: Linear algebra, matrices, and you

But that's not necessarily true. If you have a 2 x 2 matrix, the possible matrices I see working in addition to the identity matrix are

Err, have to edit these made a mistake

-1 0
0 -1

0 1
1 0

0 -1
-1 0

For example, if your matrix is [0 -1 : -1 0], multiplying by it's transpose is

0(0) + (-1)(-1) (0)(-1) + (-1)(0)
0(-1) + (0)(-1) (-1)(-1) + (0)(0)

Which is [1 0 : 0 1], an identity 2 x 2 matrix. I dunno if I"m doing something wrong, but I don't think we can prove it's definately an identity matrix
#6
04-21-2006, 07:05 PM
 jason1990 Senior Member Join Date: Sep 2004 Posts: 932
Re: Linear algebra, matrices, and you

If you regard all n-vectors as n x 1 matrices, then the dot product of two vectors, x and y, is just the matrix product, x^T y. This fact might be helpful.
#7
04-21-2006, 08:14 PM
 TBag Senior Member Join Date: Sep 2004 Location: In a raccoon suit Posts: 1,083
Re: Linear algebra, matrices, and you

since we're doing dot products and the matrix a is always a diagonal matrix of 1's or -1's, either going from top left to bottom right or bottom left to top right.
IE
[(-)1 0 0 : 0 (-)1 0 : 0 0 (-)1 ],
[0 0 (-)1 : 0 (-1) 0 : (-1) 0 0 ], etc

We can assume one of two things is happening.

1)
Ax = (A11 * x1) + (A22 * x2) ... (Ann * xn)
and same goes for y, replacing the x

or if the ones line up from bottom left to top right
2)
Ax = (A1n * xn) + (A2(n-1) * x(n-1) ) .... (An1 * x1)
and same goes for y,

so regardless of which path we take, in Ax (dot) Ay, we end up with (either A entry)^2(x1)(y1)+ ... + A^2(xn)(yn) which is the same as regular x (dot) y because any A entry squared will be 1.
#8
04-21-2006, 09:09 PM
 cliff Senior Member Join Date: May 2005 Posts: 108
Re: Linear algebra, matrices, and you

A is an orthogonal matrix, which mean A A^T=I=A^T A, for instance
A=1/sqrt(2)* [1 1
1 -1]
in fact there are an infinite number of such matrices (in the complex field at least) and the set of all such matrices are closed under multiplication. They show up a lot in the theory of matrices.
#9
04-21-2006, 09:14 PM
 cliff Senior Member Join Date: May 2005 Posts: 108
Re: Linear algebra, matrices, and you

A does not have to be diagonal (see my example of the Hadamard matrix in the above post), what you want here is that
Ax . By= B^T Ax . y for any matrices A and B by the definition of the inner product.
#10
04-21-2006, 11:33 PM
 jason1990 Senior Member Join Date: Sep 2004 Posts: 932
Re: Linear algebra, matrices, and you

As cliff mentioned, A does not have to be diagonal. Frankly, I think you should stop trying to dig into the entries of the matrix A. Think more abstractly. Are you aware of the formula (AB)^T = (B^T)(A^T)?

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Forum Rules
 Forum Jump User Control Panel Private Messages Subscriptions Who's Online Search Forums Forums Home Two Plus Two     Two Plus Two Internet Magazine     The Two Plus Two Bonus Program     Special Sklansky Forum     About the Forums     MOD DISCUSSION     Test General Poker Discussion     Beginners Questions     Books and Publications     Televised Poker     News, Views, and Gossip     Brick and Mortar     Home Poker     Poker Beats, Brags, and Variance     Poker Theory     Poker Legislation Coaching/Training     Stoxpoker.com     DeucesCracked.com German Forums     Poker Allgemein: Poker in general     Strategie: Holdem NL cash [German]     Strategie: Sonstige     Internet/Online [German]     BBV [German]     Small Talk [German] French Forums     Forum Francophone     Strategie [French]     BBV [French] Limit Texas Hold'em     Texas Hold'em     High Stakes Limit     Medium Stakes Limit     Small Stakes Limit     Micro Stakes Limit     Mid-High Stakes Shorthanded     Small Stakes Shorthanded     Limit-->NL PL/NL Texas Hold'em     High Stakes     Medium Stakes     Small Stakes     Micro Stakes     Full Ring Tournament Poker     MTT Strategy     High Stakes MTT     MTT Community     STT Strategy     Tournament Circuit/WSOP Other Poker     Omaha/8     Omaha High     Stud     Heads Up Poker     Other Poker Games General Gambling     Probability     Psychology     Sports Betting     Other Gambling Games     Entertainment Betting     Money Making and Other Business Discussion Internet Gambling     Internet Gambling     Internet Bonuses     Affiliates/RakeBack     Software     Poker Site Software, Skins, & Networks 2+2 Communities     Other Other Topics     The Lounge: Discussion+Review     EDF     BBV4Life Other Topics     Sporting Events     Politics     Business, Finance, and Investing     Travel     Science, Math, and Philosophy     Health and Fitness     Student Life     Golf     Video Games     Puzzles and Other Games     Laughs or Links!     Computer Technical Help     Bin Sponsored Support Forums     RakebackNetwork     RakeBackDepot     RakeReduction.com Rakeback     PokerSavvy

All times are GMT -4. The time now is 07:49 AM.