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1383:, yeah, you can get that impression from the movie. But in reality that matrix is a parallel universe. You probably haven't watched it too much, the matrix in the movie is our world as in 1999 re-created by the machines to control humans to be able to pacifically extract energy from our body. It is, of course, not physically possible, but then again, if all physics we know is what they want us to know, that could just be another control element.
791:{\displaystyle A={\begin{bmatrix}a_{0}&a_{-1}&a_{-2}&\ldots &\ldots &a_{-n+1}\\a_{1}&a_{0}&a_{-1}&\ddots &&\vdots \\a_{2}&a_{1}&\ddots &\ddots &\ddots &\vdots \\\vdots &\ddots &\ddots &\ddots &a_{-1}&a_{-2}\\\vdots &&\ddots &a_{1}&a_{0}&a_{-1}\\a_{m-1}&\ldots &\ldots &a_{2}&a_{1}&a_{0}\end{bmatrix}}}
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1130:. As for whether to call it "Matrix" or "Matrix theory", I don't have a strong opinion. If I had to choose, I'd say that "Matrix" sounds better, more fundamental, as a title. More people are likely to search for the "Matrix" page than for the "Matrix theory" page. Of course, whichever one is removed should redirect to the other.
1125:
page is now redundant. Also, different people use the term "matrix theory" to mean different things: for some, it is just the basic properties of matrices; for others, it is synonymous with linear algebra. It is by no means a consensus or even a majority that interprets "matrix theory" to mean "the
1166:
People who like to see in a matrix more than just a humble table of numbers, could make this paragraph into a stand alone section, and explain here the higher view of matrices. I think it is always better to start with the simplest definition possible (as for a matrix to be a 2D array) and then make
1180:
So, sometimes, when you are not sure about word definitions (or communication protocol standards) it might be better start with the most far from simple definition because that way you don't have to be too careful with each word. Since you are not talking about a basic thing you can forget a little
898:
The part about solving a linear system was intended as motivation (it's practical) and as an example to give me an excuse to put in some about how (some) matrices have inverses and you can multiply by them and cancel them and such. It may not have been a good way to show that you can manipulat the
1231:
Would it be more correct to say that the value of a matrix can be represented as a rectangular array of numbers rather that it is a rectangular array? Mathematics extracts an abstract structure from matrices and studies these properties, so we can have a matrix without having numbers written down,
876:
Anyway, I felt such an elementary thing as solving a linear system does not fit well in the same article as the much more abstract topics on top of this article (topics which are put in the section "Introduction" even if that is not an introduction, it is just a list of facts.). But this is my
1447:
True. About the universe being described as a Matrix I totally agree with you. Even because I am just a kid. So it's probably as you say. I was just trying to figure out what other people would think about it. Eventhough I'm quite expecting this subject to die here, I would still welcome more
842:
The material on
Algebra of Matrices was intended to demonstrate the sort of thing that can be developed for matrices without specific attention to what a matrices 'is', it applies to the abstract concepts that algebras apply to. The material on matrices for solving simultaneous equations was
858:). So, the square matrices with real entries are an algebra over the reals, because you can add and multiply matrices, and you can multiply them by real numbers. The set of all matrices is not an algebra, because not any two matrices can be multiplied. So the title was kind of misleading.
1344:
And no, a mathematical matrix does not do operations between universes. It is just a linear map between linear spaces. The universe is much more complicated than that, and serious map between universes I think would not be so elementary as a matrix vector multiplication.
1401:
Allow me add some definitions to the main article and let's see how people react to that... I haven't done this before because I got stuck with a double virus in my life, and my firefox crashed when I was about to submit it. Sorry if this comments is too irrelevant. :P
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A matrix can be identified with a linear transformation between two vector spaces. Therefore matrix theory is usually considered as a branch of linear algebra. The square matrices play a special role, because the nxn matrices for fixed n have many closure
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a rectangular array? Mathematics extracts an abstract structure from matrices and studies these properties, so we can have a matrix without having numbers written down, right? (I'm probably getting pedantic but it's more than just a bunch of numbers).
1149:
It seems there is more than one person saying a matrix is more than an array of numbers. I find this definition very satisfactory though. After you are very comfortable with this definition, you of course can move on to higher views of a matrix.
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contains not only the elementary definition and properties of matrices, but also a lot of more advanced material, including a list of many applications. And I see nothing wrong with this. But it does mean that most of the material on the
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article. If you want, you can put the linear system back. But either with the system, or without it, I think this article is fundamentally broken. It does not have coherence, or purpose. I dont't know how to fix it. 04:37, 7 Jan 2005 (UTC)
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I added some material on the algebra of matrices. Then I tried to use that material to show how matrices are used. In other words I want to show why matrices are interesting under the theory rather than just what they are (which is at
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Before I comment on why I deleted that contents, let me remark that one does not write "Algebra of
Matrices", but rather "Algebra of matrices" (downcase "m"). This is important; unfortunately I see this mistake endlessly on Knowledge.
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is needed for "Matrix theory". If the article contributors disagree and have in mind High/Top-importance content which is not naturally treated under the aforesaid articles (as well in individual articles on topics such as
1297:, through the movie. After reading and analyzing thousands of thoughts about all the theory evolving matrices I realise it have being really connecting me in the way I understand the existence of life and any other thing.
1375:
isn't necessarily bi-dimensional. We just think about it that way, in mathematics, to be able to use "very simple" matrices operations with them. They are complex, but way more simple than the complexity a universe is.
1451:
And about changing the article, it's already done. It's not really directly related to my idea of universe. It's just a non-mathematical way to describe a Matrix since for mathematical studies of it we already have
930:
I suggest we do that and make matrix theory a redirect to matrix (mathematics). It saves us the trouble of trying to figure out what goes in each article. The only danger is the combined article getting too big.
1432:. The amount of mathematics involved in describing the universe is staggering. Your belief that a matrix is helpful in describing the universe is like a kid's dream that using his toys he can build a skyscraper.
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we study in mathematics has anything to do with universes, and I can almost be sure it does, then it is more related to the movie than the impression we have from the title and its association with
1042:). But I think this is a bad idea and instead the article should be structured in such a way as to present a basic, accessible definition at the top and more complex definitions and topics later.
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1423:
Making a matrix higher dimensional does not change the fact that it is still a very very simple mapping. Too simple to even describe an atom, not to talk about the whole universe.
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Anyway, bottom line, for the article, it's good to start with simple but it's also good to get some steps and also include information on the most far we could go from the basic.
987:
I think we should not merge the articles. Rather, some things from Matrix (mathematics) which are more complicated should come here. What do you think could be transfered here?
1307:
could actually explain the whole Matrix in the movie, and in so many other histories that talks about the same idea. A whole universe generated by machines? Nope. Just about
1175:
I do agree it's usually better start with the simplest definition possible, but to be able to properly do that you have to be careful with choosing each word, each letter.
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I am not sure that is true. I think "Matrix theory" is about abstract and general properties of matrices. And solving a linear system is not that. But I could be wrong.
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representation for matrices. (I almost added LUP decomposition, without how to find the decomposition, as an further example of matrix manipulation but (
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has more elementary properties. So I would be inclided not to do any big changes on these pages. If you have other suggestions, I could implement them.
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Logic can be expressed in mathematics and many other fields. In this context, an encyclopedia, I believe we are talking about theories using
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the fact that on a basic statement each single letter could lead to miss understanding, or ambiguous thoughts, if it's not carefully choosed.
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If you want to divide the material into two articles, a basic one and a more sophisticated one, the pages should be named accordingly (like
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So this also would answer Oleg's question about the very interesting question on merging or not both
Articles. I agree it's not even good
854:
Now, to my remarks. You see, the word "algebra" has many meanings. In math, an algebra is a ring which is a module over another ring (see
1562:) the article is more of a stub than a "start". In addition, at least the current content fails to clarify why an article separate from
1300:
Don't get away thinking this is irrelevant. I believe, through deep logic, it is more relevant that it may look like at first sight.
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1543:, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.
975:
I would suggest you put the link above on your watchlist, and you could follow that link and maybe we can start a discussion.
1476:
Lilar recently edited parts of this article transforming it into an amusing and informative parody of its former self.
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I interpreted it as 'matrix' is the noun and 'matrix theory' is what to do with a matrix. RJFJR 04:06, Jan 7, 2005 (UTC)
33:
1067:
Sorry, somehow I missed your reponse. I probably won't do it in the near future. At the moment I am more interested in
1315:, and its respective basic operations, actually tells me about a mathematical way to do operations between universes.
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right? (I'm probably getting pedantic but it's more than just a bunch of numbers). RJFJR 22:04, Dec 25, 2004 (UTC)
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intended to demonstrate the motivation for matrices and matrix theory; it was intentionally a simple example.
1339:. There, I think they use the word "Matrix" to mean "womb" or something like that (as translated from Latin).
1052:
What you say makes sense (both options you suggest). I agree. Would you be willing to do the reorganization?
1575:), please do revert my change. However, if no such topics emerge, I would suggest merging this with Matrix.
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1015:. Then perhaps certain parts of this new article should be put into subarticles. See my latest posting at
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1549:* Needs history, motivation, much more on applications, oeverveiw fo theroems linked to in "See also"...
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Should the pre-Lilar changes be kept as Matrix Theory (math) and the parody as Matrix Theory (film)?
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Thanks for your reply, but I think you haven't really stop to get a deeper thought on this subject.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
1322:. I might be going way too far, but I do feel it is the right direction of expanding the theory.
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It's been four years, so I don't know if any of you are reading this, but at least right now,
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Please don't add anything to the article yet, I am not sure you know what you are saying.
1371:. I'm talking about thinking beyond that, as a basic line on how things could happen. A
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I'll be a little invasive in here and change one "little" aspect in the main article.
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I thought moving things myself. But somehow I think things are fine the way they are.
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I moved the part about answering subscripts inside a math tag to the above section.
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Last edited at 16:37, 14 June 2007 (UTC). Substituted at 21:51, 26 June 2016 (UTC)
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where I started a discussion on this subject. And welcome by the way :)
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Anyway, once again, thanks for your prompt answer and caring, Oleg! :)
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I'm just wondering if anyone else got somewhere around this point of
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So I'll basically just change the main article to update this idea.
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Would it be more correct to say that the value of a matrix can be
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Talk:Matrix (mathematics)#Matrix (mathematics) vs. matrix theory
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or whichever minor things we might have at a first impression.
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disambiguation page to make it clear what's the main article.
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to merge, as it would be better expand the main article into
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Algebra of
Matrices and application to simultaneous equations
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Split into Matrix Theory (math) and Matrix Theory (film)?
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Should we merge Matrix theory into Matrix (mathematics)?
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I don't think the matrix theory has anything to with
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and use it to link others. Also we could change the
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1459:But that should be "discussed" on the other topic.
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Is there a way to use subscripts in a <math: -->
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Is there a way to use subscripts in a <math: -->
1558:With the current content (essentially a subset of
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145:as a rectangular array of numbers rather that it
1126:advanced aspects of matrices". Given all this,
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1261:. So, that should be the field used to explain
1533:The comment(s) below were originally left at
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1128:there is a strong case for merging the pages
1094:is a summary of more advanced things, while
368:{\displaystyle {\begin{bmatrix}x<sub: -->
938:Today I got a message which I paste below.
415:The answer is yes! See the source of this:
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1363:I do understand perfectly how simple the
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951:Hi, I have noticed your discussion on
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1251:. After all, it is being compared to
963:. Perhaps you want to have a look at
880:I honestly don't know how to fix the
92:This redirect is within the scope of
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7:
955:. I am having similar problems with
877:opinion, you might think otherwise.
411:tag? RJFJR 22:10, Dec 25, 2004 (UTC)
1602:Redirect-Class mathematics articles
1237:Yes, I believe it is more correct.
38:It is of interest to the following
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112:Knowledge:WikiProject Mathematics
1607:NA-priority mathematics articles
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903:) I felt that was too far off.)
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1311:. The little I do know about
1295:Matrix Theory Discussion Page
1209:04:31, 16 November 2005 (UTC)
919:There isn't much left of the
168:04:34, 16 November 2005 (UTC)
106:and see a list of open tasks.
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1199:can get really surprising.
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1379:As about the movie and a
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405:to answer your question:
1573:Cayley-Hamilton theorem
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