Change of basis: Revision history

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curprev 10:4010:40, 2 October 2024‎ 131.111.185.7 talk‎ 17,862 bytes −1‎ Removed unneccessary comma undo

curprev 06:2306:23, 31 August 2024‎ Abstreal talk contribs‎ m 17,863 bytes +2‎ Fixed grammar undo Tags: Visual edit Mobile edit Mobile web edit

curprev 09:2009:20, 23 August 2024‎ D.Lazard talk contribs‎ 17,861 bytes 0‎ Reverted 1 edit by 218.215.216.108 (talk): Changing from "new" to "old" seems silly. However, I admits that it may be confusing (but this unavoidable) that the change of basis matrix expresses the old coordinates in terms of the new ones undo Tags: Twinkle Undo
curprev 09:0509:05, 23 August 2024‎ 218.215.216.108 talk‎ 17,861 bytes 0‎ In the previous version of this page, the conventions "from" and "to" were reversed in the description of change of basis. If a column vector x represents v with respect to the basis B_1, and a column vector y represents v with respect to the basis B_2, then the change of basis matrix "from" B_1 "to" B_2 satisfies Ax = y. This is the standard convention in every linear algebra text. If Gilbert Strang says something different in the referenced MIT lecture, he probably just misspoke. undo Tags: Reverted Visual edit

curprev 05:0005:00, 3 June 2024‎ Bernanke's Crossbow talk contribs‎ 17,861 bytes +83‎ →‎See also: Chirgwin-Coulson weights undo

curprev 07:0307:03, 15 May 2024‎ 150.241.255.134 talk‎ 17,778 bytes −4‎ →‎Bilinear forms: Corrected a mistake undo

curprev 22:1322:13, 31 March 2024‎ Netrapt talk contribs‎ m 17,782 bytes +1‎ fix spelling ft:term->terms undo

curprev 12:4812:48, 23 February 2024‎ 130.149.15.201 talk‎ 17,781 bytes −11‎ fixed grammar undo Tag: Visual edit

curprev 06:5806:58, 12 January 2024‎ Gvgmer talk contribs‎ 17,792 bytes −7‎ No edit summary undo

curprev 14:5014:50, 26 July 2023‎ 130.73.24.94 talk‎ 17,799 bytes +4‎ →‎Bilinear forms undo

curprev 14:4514:45, 30 October 2022‎ D.Lazard talk contribs‎ 17,795 bytes +50‎ →‎Change of basis formula: revert and avoiding the confising "formally" undo
curprev 13:5813:58, 30 October 2022‎ MFH talk contribs‎ 17,745 bytes +13‎ →‎Change of basis formula: changed "formally...is" to "sometimes...taken as". The order of the basis vectors is crucial for coordinates to make sense, unless you index coordinates by vectors instead of integers, which is extremely rare. undo

curprev 14:2214:22, 9 October 2022‎ D.Lazard talk contribs‎ 17,732 bytes 0‎ Reverted 1 edit by Veerpratapsingh (talk): Wrong change undo Tags: Twinkle Undo
curprev 12:2212:22, 9 October 2022‎ Veerpratapsingh talk contribs‎ m 17,732 bytes 0‎ →‎Example undo Tag: Reverted

curprev 12:0512:05, 17 August 2022‎ 200.137.2.54 talk‎ 17,732 bytes 0‎ No edit summary undo Tags: Manual revert Mobile edit Mobile web edit
curprev 12:0312:03, 17 August 2022‎ 200.137.2.54 talk‎ 17,732 bytes 0‎ No edit summary undo Tags: Reverted Mobile edit Mobile web edit

curprev 04:4804:48, 30 March 2022‎ 2600:6c44:777f:73d5:e45b:c6ba:6688:e849 talk‎ 17,732 bytes +3‎ →‎Endomorphisms undo Tag: Visual edit

curprev 12:4512:45, 18 February 2022‎ D.Lazard talk contribs‎ 17,729 bytes −5‎ Changing short description from "Change of coordinates for a vector space" to "Coordinate change in linear algebra" (Shortdesc helper) undo
curprev 05:2005:20, 18 February 2022‎ Anita5192 talk contribs‎ 17,734 bytes −41‎ We might as well change all of them: column matrix → column vector. undo
curprev 03:5103:51, 18 February 2022‎ Jcbowmanab talk contribs‎ m 17,775 bytes −1‎ No edit summary undo

curprev 15:2915:29, 5 February 2022‎ D.Lazard talk contribs‎ 17,776 bytes −166‎ Reverted 1 edit by Ronvdburg (talk): MOS:VAR no strong reasons for changing a valid notation. Also, in this contex, upperscripts may be confused with exponents, and the standard notation for matrices is with two lowerscripts undo Tags: Twinkle Undo
curprev 15:1615:16, 5 February 2022‎ Ronvdburg talk contribs‎ 17,942 bytes +166‎ →‎Change of basis formula: Vectors ars formatted in bold face to distinguish them from scalars. Furthermore, using superscript for contravariant indices and lowerscript for covariant indices makes is easier to read. undo Tags: Reverted Mobile edit Mobile app edit Android app edit

curprev 12:5212:52, 6 November 2021‎ Odedantar talk contribs‎ 17,776 bytes 0‎ →‎Endomorphisms: Fixed a typo :) undo Tags: Mobile edit Mobile web edit

curprev 14:2514:25, 18 August 2021‎ D.Lazard talk contribs‎ 17,776 bytes 0‎ →‎Bilinear forms: see talk undo
curprev 07:4707:47, 18 August 2021‎ D.Lazard talk contribs‎ 17,776 bytes 0‎ →‎Endomorphisms: ditto undo
curprev 07:4607:46, 18 August 2021‎ D.Lazard talk contribs‎ 17,776 bytes 0‎ →‎Linear maps: fixing an error (see talk) undo

curprev 13:4513:45, 15 July 2021‎ 109.119.212.192 talk‎ 17,776 bytes +21‎ →‎Change of basis formula: missing verb, replaced pronoun with more explicit phrase undo

curprev 07:0107:01, 14 July 2021‎ Fgnievinski talk contribs‎ 17,755 bytes +47‎ →‎See also undo

curprev 02:4802:48, 11 June 2021‎ 2600:1700:42c1:8540:110e:19aa:1eb7:9dd4 talk‎ 17,708 bytes 0‎ →‎Bilinear forms: Changed (P^TBP)^T = P^TB^TP to (PBP^T)^T = PB^TP^T to be consistent with the correction from P^TBP to PBP^T which I published a minute ago. undo
curprev 02:4202:42, 11 June 2021‎ 2600:1700:42c1:8540:110e:19aa:1eb7:9dd4 talk‎ 17,708 bytes 0‎ →‎Bilinear forms: Same minor change as in the previous two section which I've just published---corrected "matrix on the new basis" from P^TBP to PBP^T. undo
curprev 02:3602:36, 11 June 2021‎ 2600:1700:42c1:8540:110e:19aa:1eb7:9dd4 talk‎ 17,708 bytes 0‎ →‎Endomorphisms: Section claimed L = P^{-1}MP is the matrix on the new basis. I changed it to L = PMP^{-1}. Note that M = P^{-1}LP is the matrix on the old basis in terms of L, which may have contributed to the mistake. undo
curprev 02:3502:35, 11 June 2021‎ 2600:1700:42c1:8540:110e:19aa:1eb7:9dd4 talk‎ 17,708 bytes 0‎ →‎Linear maps: Section claimed L = P^{-1}MQ is the matrix on the new basis. I changed it to L = PMQ^{-1}. Note that M = P^{-1}LQ is the matrix on the old basis in terms of L, which may have contributed to the mistake. undo

curprev 15:5815:58, 21 May 2021‎ Coxy1989 talk contribs‎ 17,708 bytes +1‎ →‎Example undo
curprev 15:5615:56, 21 May 2021‎ Coxy1989 talk contribs‎ 17,707 bytes −4‎ →‎Example undo

curprev 09:4709:47, 13 April 2021‎ 84.81.5.147 talk‎ 17,711 bytes 0‎ →‎In terms of linear maps undo

curprev 19:2019:20, 6 April 2021‎ Anita5192 talk contribs‎ m 17,711 bytes −4‎ →‎Linear maps: Copy edit: removed superfluous word, "Let." undo
curprev 15:1715:17, 6 April 2021‎ 73.206.3.234 talk‎ 17,715 bytes 0‎ →‎Linear maps: fixed typo that misid’ed size of Q undo Tags: Mobile edit Mobile web edit

curprev 12:2612:26, 20 March 2021‎ D.Lazard talk contribs‎ 17,715 bytes −557‎ Undid revision 1013161763 by Hellacioussatyr (talk) MOS:VAR: The use of bf for vectors is common, but is not a rule. Moreover, here, bf was used consistently for coordinate vectors and matrices, while italics were used for elements of a vector space. This is destroyed by the edit undo Tag: Undo
curprev 10:5610:56, 20 March 2021‎ Hellacioussatyr talk contribs‎ 18,272 bytes +557‎ Boldfaced vector variables undo Tags: Reverted 2017 wikitext editor

curprev 01:3001:30, 2 March 2021‎ Tom.Reding talk contribs‎ 17,715 bytes +20‎ +{{Authority control}} (1 ID from Wikidata), WP:GenFixes on undo Tag: AWB

curprev 13:2313:23, 17 February 2021‎ Seventhsister23 talk contribs‎ m 17,695 bytes +1‎ →‎In terms of linear maps undo

curprev 20:3520:35, 9 February 2021‎ Hellacioussatyr talk contribs‎ 17,694 bytes +1‎ →‎Bilinear forms undo Tags: Mobile edit Mobile web edit Advanced mobile edit
curprev 20:3420:34, 9 February 2021‎ Hellacioussatyr talk contribs‎ 17,693 bytes −14‎ →‎Linear maps undo Tags: Mobile edit Mobile web edit Advanced mobile edit
curprev 20:3120:31, 9 February 2021‎ Hellacioussatyr talk contribs‎ 17,707 bytes −13‎ No edit summary undo Tags: Mobile edit Mobile web edit Advanced mobile edit

curprev 10:5810:58, 3 February 2021‎ D.Lazard talk contribs‎ 17,720 bytes −1‎ →‎Bilinear forms: typo and tweaks undo
curprev 10:5210:52, 3 February 2021‎ D.Lazard talk contribs‎ 17,721 bytes +1,046‎ →‎Bilinear forms: fixing an error, and clarifying the link with spectral theorem; see my talk page undo

curprev 22:2522:25, 2 February 2021‎ D.Lazard talk contribs‎ 16,675 bytes −145‎ →‎Bilinear forms: Partial revert: the spectral theorem is about diagonalisation of endomorphisms, not of bilinear forms. So, it is out of scope in this section. Moreover, mentioning it in this section is confusing, as the eigenvalues of a bilinear form are defined only up to a square. undo
curprev 22:1522:15, 2 February 2021‎ Anita5192 talk contribs‎ m 16,820 bytes +1‎ →‎Bilinear forms: ce undo
curprev 21:4821:48, 2 February 2021‎ BTotaro talk contribs‎ 16,819 bytes +128‎ Links added undo
curprev 18:3418:34, 2 February 2021‎ D.Lazard talk contribs‎ 16,691 bytes +1,213‎ →‎Bilinear forms: rewritten undo

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