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Author Topic: Who understands the matrix equation Ax=b?  (Read 5481 times)

Offline jeffreyH

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Who understands the matrix equation Ax=b?
« on: 16/01/2016 16:58:48 »
To some this may sound like a trivial question. Others won't know what I am talking about. This is the crux of a problem with physics forums. If you don't know the answer and simply come to a forum such as this to have questions answered then I can see no problem with that. That is a learning exercise. If you don't know the answer and you are trying to postulate a new 'theory' to revolutionize physics then you have real problems with your understanding of the subject. You could always google it of course but you may miss the subtleties.


 

Offline Bored chemist

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Re: Who understands the matrix equation Ax=b?
« Reply #1 on: 16/01/2016 17:32:21 »
It's not just a problem on science fora.
If you are not clear people don't understand you and it doesn't matter if it's science or flower arranging.
You have to put the effort into framing a sensible question.
 

Offline jeffreyH

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Re: Who understands the matrix equation Ax=b?
« Reply #2 on: 16/01/2016 17:37:35 »
That's a very good point.
 

Offline jeffreyH

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Re: Who understands the matrix equation Ax=b?
« Reply #3 on: 17/01/2016 01:11:23 »
Just to add more to the mix we can rearrange the equation as x=A-1b. How does this relate to the reduced row echelon form and the identity matrix?
 

Offline Colin2B

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Re: Who understands the matrix equation Ax=b?
« Reply #4 on: 17/01/2016 09:31:06 »
Just to add more to the mix we can rearrange the equation as x=A-1b. How does this relate to the reduced row echelon form and the identity matrix?
I assume you are not one of those seeking answers, but know the answer, but like me get irritated with certain people who think they know physics and maths and so make silly challenges to physics eg relativity without really understanding that theory.
I shall mention no names!

To be honest I'm no longer irritated as I realise they do not wish to learn, just to see their words.
 

Offline evan_au

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Re: Who understands the matrix equation Ax=b?
« Reply #5 on: 17/01/2016 09:58:49 »
This could be read as a rhetorical question:
Quote from: jeffreyH
Who understands the matrix equation Ax=b?

But this addendum makes it sound like a request for a simple explanation of matrix arithmetic:
Quote
Just to add more to the mix we can rearrange the equation as x=A-1b. How does this relate to the reduced row echelon form and the identity matrix?

So if you are looking for a simple explanation of solving matrix equations, this site explains most things quite well:
https://www.khanacademy.org/math/precalculus/precalc-matrices/solving-equations-with-inverse-matrices/v/matrix-equations-systems
 

Offline jeffreyH

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Re: Who understands the matrix equation Ax=b?
« Reply #6 on: 17/01/2016 13:37:13 »
Thanks Evan that is very likely a good place to start. Since I don't need to read it I take it on trust.
 

Offline dhjdhj

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Re: Who understands the matrix equation Ax=b?
« Reply #7 on: 17/01/2016 15:10:44 »
I am trying to fathom why you asked a question to which you obviously know the answer. The manipulation of matrix equations is obviously critical to the understanding of the mathematics of advanced physics, but so is advanced calculus and three dimensional geometry. Now some of us non physicists in trying to understand the status quo get lost in the maths either through lack of knowledge or in my case lack of practise. Its many years since I was required to do it. Some of us have ideas that seem to us OK, but we need you to tell us why they are not. Some of us have tried to study the basics as much as possible (in my case even buying expensive text books), but much of it is statement of fact, rather than how that fact was established. So theories ( or more correctly hunches) inevitably follow.
They are of course wrong, but why? It really comes down to what you see is the purpose of the forum. If it for professionals to exchange ideas. Then so be it, there is no point in me or other 'crackpots' contributing. If it is to promote alternatives, there is no point in professionals contributing. I believe it is neither of the above and that it should be an opportunity for interchange between both groups. It is easier to get a date with David Cameron than find a physicist to discuss any ideas you may have. I find the concept of needing to pass the matrix exam before you can discuss physics in a meaningful way a little bit upsetting and may actually prevent future questions through fear of embarrassment. Do you think we should only ask questions of a controversial nature to which we know the answer?
 

Offline Thebox

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Re: Who understands the matrix equation Ax=b?
« Reply #8 on: 17/01/2016 15:28:07 »
To some this may sound like a trivial question. Others won't know what I am talking about. This is the crux of a problem with physics forums. If you don't know the answer and simply come to a forum such as this to have questions answered then I can see no problem with that. That is a learning exercise. If you don't know the answer and you are trying to postulate a new 'theory' to revolutionize physics then you have real problems with your understanding of the subject. You could always google it of course but you may miss the subtleties.

I searched for this, I have no idea of what it means or what it is trying to explain, I have never learnt this so can not make any sort of assumptions,

it says that A = 3*3 xyz. I have no idea what that suppose to mean to start with, to me it means nothing, you cant have 3*3 xyz


p.s and not knowing this is not relative to any idea.


science keeps doing this , and never listens, that is the problem. Science is not the ''gods'' of thought, ''we'' can think just as well .




« Last Edit: 17/01/2016 15:31:35 by Thebox »
 

Offline jeffreyH

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Re: Who understands the matrix equation Ax=b?
« Reply #9 on: 17/01/2016 15:40:31 »
I am trying to fathom why you asked a question to which you obviously know the answer. The manipulation of matrix equations is obviously critical to the understanding of the mathematics of advanced physics, but so is advanced calculus and three dimensional geometry. Now some of us non physicists in trying to understand the status quo get lost in the maths either through lack of knowledge or in my case lack of practise. Its many years since I was required to do it. Some of us have ideas that seem to us OK, but we need you to tell us why they are not. Some of us have tried to study the basics as much as possible (in my case even buying expensive text books), but much of it is statement of fact, rather than how that fact was established. So theories ( or more correctly hunches) inevitably follow.
They are of course wrong, but why? It really comes down to what you see is the purpose of the forum. If it for professionals to exchange ideas. Then so be it, there is no point in me or other 'crackpots' contributing. If it is to promote alternatives, there is no point in professionals contributing. I believe it is neither of the above and that it should be an opportunity for interchange between both groups. It is easier to get a date with David Cameron than find a physicist to discuss any ideas you may have. I find the concept of needing to pass the matrix exam before you can discuss physics in a meaningful way a little bit upsetting and may actually prevent future questions through fear of embarrassment. Do you think we should only ask questions of a controversial nature to which we know the answer?

You have 1. Formulated some ideas. 2. Investigated the mathematical tools. 3. Looked at how those ideas may fit with established observations or theories. 4. Come to a physics forum to have your ideas scrutinized and criticized by your peers. 5. Appear willing to accept criticism in order to help improve your ideas.

Why do you think that my comments are in any way aimed at you?
 

Offline jeffreyH

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Re: Who understands the matrix equation Ax=b?
« Reply #10 on: 17/01/2016 15:45:46 »
To some this may sound like a trivial question. Others won't know what I am talking about. This is the crux of a problem with physics forums. If you don't know the answer and simply come to a forum such as this to have questions answered then I can see no problem with that. That is a learning exercise. If you don't know the answer and you are trying to postulate a new 'theory' to revolutionize physics then you have real problems with your understanding of the subject. You could always google it of course but you may miss the subtleties.

I searched for this, I have no idea of what it means or what it is trying to explain, I have never learnt this so can not make any sort of assumptions,

it says that A = 3*3 xyz. I have no idea what that suppose to mean to start with, to me it means nothing, you cant have 3*3 xyz


p.s and not knowing this is not relative to any idea.


science keeps doing this , and never listens, that is the problem. Science is not the ''gods'' of thought, ''we'' can think just as well .

Physics is a fascinating subject. As things become clearer it also becomes apparent just how little we actually know. Does that give us a licence to indulge in wild and uninformed speculation? You may say yes. Well if that had always been the case then we would still be living in a fifteenth century society.
 

Offline Thebox

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Re: Who understands the matrix equation Ax=b?
« Reply #11 on: 17/01/2016 16:04:26 »


Physics is a fascinating subject. As things become clearer it also becomes apparent just how little we actually know. Does that give us a licence to indulge in wild and uninformed speculation? You may say yes. Well if that had always been the case then we would still be living in a fifteenth century society.


It depends how you define wild and uninformed, science presumes some ideas are wild,but the opp knows very well what they are on about.

In this thread , I have read from looking 3*3 xyz , this sounds multi-dimensional , when n-dimensional explains .

added - what Matrix are you referring to?

 I don't know if this helps you Jeffrey but I have done you a diagram.












« Last Edit: 17/01/2016 16:22:11 by Thebox »
 

Offline jeffreyH

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Re: Who understands the matrix equation Ax=b?
« Reply #12 on: 17/01/2016 16:20:03 »
The A in the equation is an m by n matrix with m rows and n columns. The x is a vector with n rows and 1 column.The resulting b is also a vector with m rows and 1 column. This means that the two vectors x and b may not be of the same dimension. They will be if matrix A is a square matrix so that m = n but not if this matrix is rectangular so that m <> n. Nowhere does it state that the matrix A has to be 3 rows by 3 columns.
 

Offline Thebox

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Re: Who understands the matrix equation Ax=b?
« Reply #13 on: 17/01/2016 16:27:11 »
The A in the equation is an m by n matrix with m rows and n columns. The x is a vector with n rows and 1 column.The resulting b is also a vector with m rows and 1 column. This means that the two vectors x and b may not be of the same dimension. They will be if matrix A is a square matrix so that m = n but not if this matrix is rectangular so that m <> n. Nowhere does it state that the matrix A has to be 3 rows by 3 columns.


arrr, ok, I now understand, yes I now understand it is easy, similar to my poker idea. You have a 3 dimension cube matrix, XYZ, at each point in the matrix there is a variable, does this sound about right for the Matrix you are talking about?


So A is area and X is a piece of paper stacked on a piece of paper and so on?
« Last Edit: 17/01/2016 16:37:04 by Thebox »
 

Offline dhjdhj

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Re: Who understands the matrix equation Ax=b?
« Reply #14 on: 17/01/2016 16:36:51 »
Thank you Jeffrey. I didn't actually think it was directed at me specifically but I was trying to explain how difficult it is to find any other means to bounce ideas other than these fora. So if I ask more dumb questions that's OK then? However like you I do get irritated when perfectly Ok answers are ignored for some ones own ill thought out dogma.
 

Offline Thebox

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Re: Who understands the matrix equation Ax=b?
« Reply #15 on: 17/01/2016 16:38:43 »
Thank you Jeffrey. I didn't actually think it was directed at me specifically but I was trying to explain how difficult it is to find any other means to bounce ideas other than these fora. So if I ask more dumb questions that's OK then? However like you I do get irritated when perfectly Ok answers are ignored for some ones own ill thought out dogma.

I have tried your approach, trying to stand out doe's not work.   Just keep plugging at the ideas and hope someone who has influence takes a shine for your ideas. Thatis all you could hope for, perhaps a co-write.
 

Offline jeffreyH

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Re: Who understands the matrix equation Ax=b?
« Reply #16 on: 17/01/2016 16:40:43 »
Thank you Jeffrey. I didn't actually think it was directed at me specifically but I was trying to explain how difficult it is to find any other means to bounce ideas other than these fora. So if I ask more dumb questions that's OK then? However like you I do get irritated when perfectly Ok answers are ignored for some ones own ill thought out dogma.

I'm glad we sorted that out then.
 

Offline Thebox

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Re: Who understands the matrix equation Ax=b?
« Reply #17 on: 17/01/2016 16:42:20 »
Thank you Jeffrey. I didn't actually think it was directed at me specifically but I was trying to explain how difficult it is to find any other means to bounce ideas other than these fora. So if I ask more dumb questions that's OK then? However like you I do get irritated when perfectly Ok answers are ignored for some ones own ill thought out dogma.

I'm glad we sorted that out then.

No comment, I know what science thinks of me, that is why I put in little effort, nobody ever really listens, so why should I care , I know deep down I am wasting my time.
 

Offline timey

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Re: Who understands the matrix equation Ax=b?
« Reply #18 on: 17/01/2016 16:44:05 »
Is advanced physics based on observation, or is it based on mathematics?

What if there is another, better means to equating the matrix equation, or the concepts a matrix equation describes?

Why would one need to understand the matrix equation to understand relativity?  There are umpteen books that make full description without reference to maths.  Combining the facts with observation and employing ones imagination, a visual representation is apparent.  Some people are better at this than others... some may need the mathematical representation because they are not good at visual representation.

What would have happened if the person who started looking at round things with a different perspective had not done so?  Would we still be a society without the wheel?
I'm pretty damn certain that the wheel was not mathematically derived!

There are many ways to skin a cat... the best mathematical procedure for doing so is arbitrary.  Mathematics are not concepts and are only as good as the concepts they are attached to.  It is visionary people who come up with concepts, and mathematics is purely the tool with which one concept can be checked against another.

Do you think there is a mathematical formula for the physical act of looking so far down ones own nose that one can't see beyond one's own face?  I'm quite sure there must be a 'constant' in there somewhere!
 

Offline jeffreyH

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Re: Who understands the matrix equation Ax=b?
« Reply #19 on: 17/01/2016 16:52:47 »
The A in the equation is an m by n matrix with m rows and n columns. The x is a vector with n rows and 1 column.The resulting b is also a vector with m rows and 1 column. This means that the two vectors x and b may not be of the same dimension. They will be if matrix A is a square matrix so that m = n but not if this matrix is rectangular so that m <> n. Nowhere does it state that the matrix A has to be 3 rows by 3 columns.


arrr, ok, I now understand, yes I now understand it is easy, similar to my poker idea. You have a 3 dimension cube matrix, XYZ, at each point in the matrix there is a variable, does this sound about right for the Matrix you are talking about?


So A is area and X is a piece of paper stacked on a piece of paper and so on?

OK. Say we have 3 equations

2x + y - 4z = 3
4x + 5y - z = -6
       3y - 3z = 50

What values for x, y and z solve these equations?

Matrix A hold the coefficients (the multipliers of x, y and z)

2    1   -4
4    5   -1
0    3    3

b is the column vector containing the results.

3
-6
50+

the vector x is then
x
y
z

I leave it to the reader to pursue the operations necessary for a solution. (There may of course be no solution).
 

Offline jeffreyH

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Re: Who understands the matrix equation Ax=b?
« Reply #20 on: 17/01/2016 17:01:11 »
If all you have is a hammer everything looks like a nail. If all you have is the description of a hammer how do you even know what a nail is?
 

Offline Thebox

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Re: Who understands the matrix equation Ax=b?
« Reply #21 on: 17/01/2016 17:03:56 »




OK. Say we have 3 equations

2x + y - 4z = 3
4x + 5y - z = -6
       3y - 3z = 50


Hmm,


you are saying 2 * vector(x) +y-(4*z)=3?

what happened to A?

Sorry you threw me off track, I am not even sure I am picturing the matrix correctly you did not answer.

A is area X is a vector? 

2*X = 2?

is Y 5?








« Last Edit: 17/01/2016 17:08:59 by Thebox »
 

Offline dhjdhj

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Re: Who understands the matrix equation Ax=b?
« Reply #22 on: 17/01/2016 17:12:59 »
I think there may more of a grain of truth in Timey's post . Mathematics may have become the primary partner in the marriage with concept. Dirac took the view that structure didn't matter as long as the maths was correct. I can't reconcile myself to that view. Even the fact that Heisenberg and Schrodinger ended up with compatible maths from different concepts gives me pause for thought. From what I have read there have been notable physicists who were not good at maths. Faraday for a start. Of course if the maths is wrong, the idea cant be right ,but if the maths is right it does not necessarily mean the idea is right. I take it Jeffrey you want some one specific to solve your problem.
 

Offline timey

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Re: Who understands the matrix equation Ax=b?
« Reply #23 on: 17/01/2016 17:16:43 »
If all you have is a hammer everything looks like a nail. If all you have is the description of a hammer how do you even know what a nail is?

A hammer is a tool, and so is a nail.  Play with your tools all you like, they are fun I must admit, but if you are to use your tools to build a representation of the universe, it is necessary to refer back to reality.

The reality is that the tools haven't quite been able to fully represent the reality, so why are you blowing a trumpet over the tools?
 

Offline Thebox

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Re: Who understands the matrix equation Ax=b?
« Reply #24 on: 17/01/2016 17:17:32 »
I think there may more of a grain of truth in Timey's post . Mathematics may have become the primary partner in the marriage with concept. Dirac took the view that structure didn't matter as long as the maths was correct. I can't reconcile myself to that view. Even the fact that Heisenberg and Schrodinger ended up with compatible maths from different concepts gives me pause for thought. From what I have read there have been notable physicists who were not good at maths. Faraday for a start. Of course if the maths is wrong, the idea cant be right ,but if the maths is right it does not necessarily mean the idea is right. I take it Jeffrey you want some one specific to solve your problem.


Jeffrey already knows the answer, I think he is trying to educate us a bit, why not try to solve the answer, I could do it in ''time'' by simply trial and error, going through all the numbers until I find the value of z and x that fits the answer.

Quite easy but time consuming, I don't know the answer but I could work it out with ''time'' .



2x + y - 4z = 3
4x + 5y - z = -6
       3y - 3z = 50


first answer 3, so we can try 2*x+Y-(4*z)=3        we can try x at 1, and we can try z at 1 and Y at 5 to give 3 as the answer

4x + 5y - z = -6  we can try the values, we conclude they dont fit, so we know our answer to the first one is wrong,


and so until we get the answer





« Last Edit: 17/01/2016 17:23:30 by Thebox »
 

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Re: Who understands the matrix equation Ax=b?
« Reply #24 on: 17/01/2016 17:17:32 »

 

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