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multiply matrices, which goes beyond that. Then, it again says that "major application of matrices is to represent linear transformations" (should probably read linear map), so if this is just the major application, calendar sheets would indeed fall into the category matrix. But then below under the heading "Definition" addition and multiplication are again required, and essentially all the rest of the article is about computations on matrices. Historically, Sylvester's introduction of the term also is only in the context of computability. I would argue to restrict the meaning of matrix here to those rectangular arrays of quantities that at least allow meaningful matrix multiplication, and I think that I am in line with most textbooks on that. Specifically, the introduction should reflect that explicitly. What are your thoughts on that?
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matrix" is a very clear example of this, but so are thousands of other things; a common example is that "surfaces with boundary" are not surfaces under the usual definition. (Allowing myself to follow you in an off-topic direction: in my experience as an educator, beginners need to develop intuition before they can develop rigor, not the other way around.) --
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then analyzed using linear algebra. Two examples are provided but claimed to be examples of the opposite: in combinatorics, adjacency and incidence matrices are defined as properties of discrete structures but there is a large industry of doing linear algebra with those matrices to analyze those structures. See
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It is true that infinite matrices are not matrices under the usual definitions, and also true that for many purposes it is sensible to class them with and study them alongside matrices. Roughly the same applies to matrices with 0 rows or 0 columns or both (though in some contexts they may in fact be
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Latin squares are one of my specialties and I'd be very surprised if any of my colleagues denies that they are a type of matrix. But I'm not proposing they be mentioned in the lead. The major problem is that the lead says "Without further specifications, matrices represent linear maps" but not a clue
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No, it is not right. There are multiple problems. First, "without further specification" as no meaning. Can we say "here is a matrix of numbers but you are forbidden to multiply it by a vector"? Actually, mathematics is full of examples where matrices arise from a non-linear-algebra context but are
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I have rewitten the lead for fixing this issue. I have also removed many technical details that do not belong to the lead, for getting a lead of a reasonable length. The article body still requires to be updated, in particular for inserting in it details that I have removed from the lead, which were
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The formulation "without further specification" can certainly be improved. The intended meaning if that, when one encounters the word "matrix" without any specification of the kind of matrix that is considered, this is in relation with linear algebra. This does not deny that other rectanguar arrays
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By the way, the current lead is much too long, and contains to much technical details that belong to the body. IMO, the lead must be reduced to: the preceding quotation (or a variant of it); a short paragraph linking to other kinds of matrices and stating that the remainder of the article is about
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The definition is unclear: in the very first sentence it is just a way of representation -- mathematical quantities in a rectangular array. In this sense, a calendar sheet that shows the dates of a month arranged by weeks would also be a matrix. Later comes the statement that you can add or even
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I agree that intuition should be developed before rigour. But once rigor begins, it should be really rigorous. Only when rigour is acquired, loose expressions become acceptable. So, then the article needs an intuitive introduction before the definition. I admit this would be the hardest part of
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not referred. Means it can be driven with however the way you calculate so, addition, subtraction and so on of
Matrices. Considering the one or more stands as Principal. Because it was not clearly explained by anyone so, rather been talked like what your book say so about it in this Talk page,-
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It is not possible to develop, in an encyclopedic context, a rigorous treatment of the word "matrix" that is consistent across all uses, because those uses are not consistent with each other; this is not a flaw in the way the
Knowledge article is written, it is just the way life is. "Infinite
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The section on 'History' mentions a very early use of matrices in China, then says that
Cardano 'brought the method to Europe' in the 16th century. This might be interpreted as meaning that Cardano was aware of the ancient Chinese example and then introduced it to Europe. This seems highly
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Polynomial expansion clearly can be segregated for sure to more than one Linear
Equation at its granularity, unless it reportedly dual by nature which might occur probably in Binomial Expansion very commonly. In any given non-linear equation, there exists at-least one Linearity. For anymore
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Thanks everyone for your input to create this. I believe the matrix example near the top should show the subscripts for the first two columns to be: a11, a21, a31, am1 and a12, a22, a32, am3 (the row subscripts are not indexing on the example). The last column follows the proper format.
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The point is that objects and their signs (that are mathematical objects only qua types, not qua tokens) have to be distinguished. The objects themselves don't form any rectangle, their sign tokens do. Anyway, "rectangular array" isn't clear enough. Matrices aren't literally data types.
1269:. But there subtraction isn't mentioned. Subtraction doesn't reduce to addition when we have no operation of opposite (opposite element, that is, inverse element as to addition). So we should have either subtraction or opposite among basic operations. --
834:, a matrix represents a linear map, is important enough for appearing soon and clearly in the lead. By the way, your example of Latin squares is not really convenient here, as Latin squares are rarely called matrices, at least in Knowledge article.
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Years ago, I seem to recall a
Knowledge page that showed examples of rectangular matrices that did not require SVD. I think some carried names. I've searched Knowledge and Google, and now I find nothing. Any ideas on where to find such examples?
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unlikely. If it is not the intended meaning, I suggest the text should say just that
Cardano was the first mathematician to use the method in Europe. Incidentally, the article on Cardano does not seem to mention his contribution to the subect.
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the matrices of linear algebra; a paragraph on square matrices; a paragraph on computational linear algebra and applications outside mathematics (this may be in the same paragraph, as most applications outside mathematics use computers).
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But is that suffices, I have eye sight problem, unfortunately, Yes I read determination as differentiation at first sight. So got to writ over here again. I hope you folks can feel the difference. Maybe there is one, say Nabla or so.
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are called matrices (examples are given in the same paragraph). This does not deny either that these other matrices may have hidden relations with linear algebra (examples given in a footnote). IMO, the fact that,
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Essentially every reliable source on matrices uses the phrase "rectangular array" or equivalent, there is no possibility of it not appearing early and prominently in any discussion of what a matrix is.
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It seems to me that neither infinite matrices nor empty matrices can be subsumed under the official definition, so the presentation is inconsistent. By the way, there is another generalization:
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In the case of real and complex numbers the opposite is multiplication by –1. I don't know ho far this can be generalized. In any case, this should be mentioned, I think. --
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In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, that is used to represent a
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or a property of such an object. Generally, the operations on the represented objects are reflected by corresponding matrix operations. Without further specifications,
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is provided as to what that means. The poor reader has to find their way down to the "linear transformation" section and try to decode the explanation given there.
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I have edited the "See also" section for displaying the short descriptions of the linked articles. I leave to others to decide which links are relevant here.
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This seems trivial to experienced mathematicians but I'm pretty sure that for beginners, lack of rigour can become an obstacle of understanding.
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mathematical objects. Some other wording is needed. English isn't my first language, so I cannot propose any better wording. --
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Of course they belong to the topic but I think it should be clearly and precisely stated how they relate to usual matrices.
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This is possibly a problem of your viewer. On my laptop and my i-phone, the column indices are displayed correctly (in red).
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I've tweaked the wording to avoid the (unclear, at least to me) phrase "without further specification". --
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I agree, this should be changed. And the lead contains details that should be left to the main text. --
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use of a matrix in mathematics is to represent a linear map, and then immediately give an example (say
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I agree: "array" is used here in its simple common language meaning. I have removed the wikilink. --
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Hypermatrices are mentioned briefly in the article, but under the alternative name "tensors". --
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You are of course welcome to edit the article, or to make concrete proposals for changes. --
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And oriented graphs are not graphs. I think this is no problem if this is clearly stated. --
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I disagree with Matrix addition, subtraction even if it is just
Mathematics.
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Good call D.Lazard. It is the correct on my laptop (but not on my iPhone).
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Symbols and expressions are also mathematical objects. I would suggest
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Things are not as simple as it could appear: with your suggestion, an
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Matrices are mathematical objects on their own right. --
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I have added subtraction, with other cosmetic changes.
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Then this needs more explication. "Array" is linked to
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460:Mathematics
451:mathematics
407:Mathematics
330:Peer review
148:free images
31:not a forum
1431:Categories
832:by default
690:represent
257:under the
1412:Steel1943
1355:Steel1943
571:Sadasivam
376:is rated
88:if needed
71:Be polite
21:talk page
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943:CarmenRx
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700:addition
694:; their
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621:D.Lazard
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335:Reviewed
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186:Archives
56:get help
29:This is
27:article.
969:numbers
959:Numbers
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487:on the
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142:scholar
1285:Andres
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967:. But
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851:McKay
817:McKay
779:never
365:This
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