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I disagree. In my current courses, Continuum
Mechanics and Fluid Mechanics at the University of Minnesota the term orthonormal is used quite often and found in our textbook and in a few research papers. In particular "Introduction to the Mechanics of a Continuous Medium" by Lawrence E. Malvern. It
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i would assume the line "An orthogonal matrix is a special orthogonal matrix if its determinant is +1" at the start is ment to be "An orthonormal matrix is a special orthogonal matrix if its determinant is +1" as having the sentance that "A is a special case of A" isnt really saying anything, so im
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I disagree. It's not about prescribing, it's about following definitions: "adjective word" should never mean anything other than "word that is adjective" (there are exceptions like dictatorships calling themselves "Democratic People's
Republic", but in those cases some entity decides its own name,
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This article makes two factually inaccurate statements in the opening sentences: (i) that orthogonal matrices must be real, and (ii) that the extension of the property of orthogonality to complex matrices is unitarity. Both are incorrect: orthogonality is the requirement that a matrix satisfy
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Paul's Online Math Notes' (from Lamar
University) pages on linear algebra have been taken off the Web. They have been gone at least since January 2013 and are not there today (May 26, 2013). The link to these notes should probably be removed from this article (and other articles if needed).
1600:, but it's not used.' To say it's never used would be hyperbole, but the point remains that it's not the common name. It may be frustrating that the same word ("orthogonal") in slightly different contexts can mean different things, but that's just the way it is.
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You can't just redefine "orthogonal", no matter how common it is to misuse this term. It does not make sense for "orthogonal matrix" to mean anything other than "a matrix that is orthogonal". This is similar to redefining
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The term "orthonormal" is completely standard in the phrase "orthonormal basis". And, confusingly, the columns of an "orthogonal matrix" do comprise an orthonormal basis. Despite this overlap, the phrase "orthonormal
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While orthogonal matrices with non-real elements are less commonly occurring in mathematics and the sciences than real orthogonal matrices, they do occur, and there is a literature which studies their properties (eg
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Isn't the introduction somewhat ambiguous? It says "In linear algebra, an orthogonal matrix is a square matrix with real entries whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors)." If
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I've even had one assignment requesting I find orthonormal eigen vectors. The manner in which it is mentioned in my courses implies it is standard in the field of
Aerospace Engineering. --
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The sentence "An orthogonal matrix is a special orthogonal matrix if its determinant is +1" makes perfectly sense to me, but perhaps it's easy to misread it, so I reformulated it. --
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shows a fundamental misunderstanding of what
Knowledge is supposed to do. Knowledge summarizes information that appears in reliable sources; including information is a matter of
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you can define the word "orthogonal" to have two different meanings simultaneously; it is an extremely common thing to do with a word, both inside and outside of mathematics. --
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1562:– This page describes orthonormal matrices, which a special case of orthogonal matrices, but are not the same. Orthonormal means orthogonal ("ortho") and normalized ("normal").
1483:. Orthonormal is a special case of orthogonal where the vectors are both orthogonal ("ortho") and normalized ("normal"). The current article is incorrect to equate these terms.
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Since you misinterpret the content of the MathWorld site, which I can see, I'm inclined to suspect you make the same mistake with the
Malvern text, which I cannot see. --
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However I've always been a bit confused about this. Surely the definition in terms of matrices is only true when the basis is itself orthonormal? In components
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Note this only occurs on this math article, I read many other articles with LaTeX embedded with no problems. So I doubt it's a browser issue (I use FireFox).
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942:= a^T M b, a matrix Q preserves the inner product if and only if Q^T M Q = M. Unless M is (a multiple of) the identity, such matrices are not orthogonal.
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Curiously the problem is not visible when I open the "Edit" tab where the formatting works just fine, so I'm not sure how to offer an edit / fix.
1687:. I totally agree that orthonormal matrix could have been a better name, for reasons Aaronfranke mentioned, but this is not given any weight by
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is a well-defined term, orthogonal does not mean normalized, orthogonal only means orthogonal. After the move, orthogonal can get its own page.
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The LaTeX formatting is not working correctly throughout this article. For example see the superscipted T indices near the top of the article:
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If these two terms mean the same thing, should we add the other terminology in the lead? E.g. Orthogonal matrix, or orthonormal matrix, etc.
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Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a
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The definition is with respect to a fixed inner product. It's not reasonable to expect a matrix to preserve all possible inner products.
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a direct counterexample to the statement "Stronger than the determinant restriction is the fact that an orthogonal matrix can always be
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1623:: Ki, so KiB for 1024 bytes. Similarly, the only correct terminology to refer to a matrix that is orthonormal is "orthonormal matrix".
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with this article. However, I do seem to remember having seen it used somewhere (hmm, that's a contorted verbal construction). --
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nobody owns math). My argument is that the existing sources do not matter, they are wrong. In my opinion it is irrelevant that
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for this concept. Yes, I agree the inconsistency is annoying, but it's what we have at the moment. To be frank, claiming that
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Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
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1149:"An orthogonal matrix is a square matrix whose columns and rows are orthogonal unit vectors (i.e., orthonormal vectors),"
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per the
Adumbrativus and HTinC23. This is not a close question, please find something better to do with your time. --
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I've seen "othronormal" used in courses as well. It may be a less popular alternative. I'll make a note as such.
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must also be an orthogonal matrix because the vectors are still orthogonal(but no longer orthonormal)
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after discussing it on the closer's talk page. No further edits should be made to this discussion.
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on
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I do have a JPG screenshot/snippet showing the issue, but
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can the usual 'dot product' inner product be used. At least that is how it seems to me.
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You can't just redefine "orthogonal", no matter how common it is to misuse this term.
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Surely that's incorrect. For an arbitrary noncanonical inner product <a, b: -->
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or recommend the "correct" terminology, but reflect the common usage, see e.g.
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Hello, this is my first ever comment on a Knowledge mathematics article.
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That matrix Bilingsley presents is an orthogonal matrix. Its vectors are
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A real square matrix is orthogonal if and only if its columns form an
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783:{\displaystyle det(Id)=1=det(QQ^{T})=det(Q)det(Q^{T})=det(Q)^{2}=1}
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Your matrix isnt orthogonal, so the statement does not apply.
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is an orthogonal matrix then according to the current version
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where repeated indices are summed. But the inner product of
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https://netspeak.org/#q=%5Borthogonal+orthonormal%5D+matrix
1584:. The term "orthogonal matrix" is overwhelmingly standard;
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It displays as $ Q^{\mathrm {T}}Q = QQ^{\mathrm {T}}=I,$
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Orthogonal means that the vectors are perpendicular. See
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1752:common name
1716:Aaronfranke
1679:or compare
1625:Aaronfranke
1568:Aaronfranke
1517:move review
1485:Aaronfranke
1126:Aaronfranke
1073:eigenvalues
856:—Preceding
364:dot product
150:Mathematics
141:mathematics
97:Mathematics
1804:Categories
1712:WP:SKYBLUE
1564:Orthogonal
1122:orthogonal
1081:Bilingsley
993:Properties
980:Gsspradlin
1673:prescribe
1642:of course
1526:Not moved
1067:over the
44:Not moved
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1617:kilobyte
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1325:contribs
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1295:contribs
1283:unsigned
1099:unsigned
858:unsigned
328:Kruzicka
240:365 days
206:Archives
1693:HTinC23
1287:Oward98
1077:modulus
959:Mct mht
409:Danielx
381:, with
355:of the
177:on the
68:B-class
1748:Oppose
1731:Oppose
1665:Oppose
1582:Oppose
1458:CJ7903
1408:, and
596:, and
456:Since
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169:High
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