Spectral theorem: Revision history

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curprev 23:0023:00, 22 April 2025 Mikhail Ryazanov talk contribs 25,995 bytes −253 Undid revision 1224388972 by 107.122.85.53 (talk) undo Tag: Undo

curprev 22:2822:28, 21 April 2025 Henrik Schumacher talk contribs m 26,248 bytes −30 Of course, Dirac delta distributions lie in some Banach space, e.g., in that dual space of the Banach space of continuous functions. The reference to Banach spaces here was a read hering. As a side note: the elements of Lebesgues space are no "classical functions", either, but rather _equivalence classes_ of functions. But I think the remainder of the statement can be left as is, nonetheless. undo

curprev 00:0500:05, 13 December 2024 Aoa7386 talk contribs m 26,278 bytes −30 No edit summary undo

curprev 16:2416:24, 15 November 2024 Magyar25 talk contribs 26,308 bytes −50 →Spectral subspaces and projection-valued measures: Harmonize variable letters undo Tag: Visual edit
curprev 16:1816:18, 15 November 2024 Magyar25 talk contribs 26,358 bytes +1,257 →Multiplication operator version: Relate to finite-dimensional spectral theorem undo Tag: Visual edit

curprev 02:5902:59, 18 May 2024 107.122.85.53 talk 25,101 bytes +253 fixed numerous minor math typesetting errors undo Tag: Reverted

curprev 06:5006:50, 10 May 2024 David Eppstein talk contribs 24,848 bytes −34 →Multiplication operator version: simplify broken link undo

curprev 14:5914:59, 26 April 2024 92.85.80.120 talk 24,882 bytes −988 →Hermitian maps and Hermitian matrices: Removed a lot of mistaken mathematics. undo

curprev 05:3105:31, 16 March 2024 Roffaduft talk contribs 25,870 bytes +79 Cosmetic: removed capitalization, added wiki hyperlinks, removed redundancies. Fixed minor error in SVD subsection, in line with SVD main wiki article undo

curprev 16:1516:15, 15 March 2024 Roffaduft talk contribs 25,791 bytes −26 Undid revision 1213831902 by 2001:6B0:17:FC17:209E:BD88:302C:DF24 (talk) Please add source undo Tag: Undo
curprev 11:2611:26, 15 March 2024 2001:6b0:17:fc17:209e:bd88:302c:df24 talk 25,817 bytes +26 →Spectral decomposition and the Singular value decomposition undo Tag: Reverted

curprev 05:4505:45, 4 March 2024 Embyarby talk contribs 25,791 bytes +1 Typo undo

curprev 21:5121:51, 18 February 2024 76.117.237.194 talk 25,790 bytes +1 Fix typo in heading undo
curprev 06:0306:03, 18 February 2024 Roffaduft talk contribs m 25,789 bytes +14 →Unbounded self-adjoint operators: added wiki hyperlink undo

curprev 21:1521:15, 10 February 2024 Magikarp23 talk contribs m 25,775 bytes −11 →Hermitian implies square matrix, removes redundancy undo

curprev 10:1710:17, 24 January 2024 Roffaduft talk contribs m 24,478 bytes +21 →Compact self-adjoint operators: fixed wiki hyperlink undo
curprev 08:5708:57, 24 January 2024 Roffaduft talk contribs m 24,457 bytes +1 →Spectral subspaces and projection-valued measures: purely cosmetic, to avoid symbol confusion. undo
curprev 08:5108:51, 24 January 2024 Roffaduft talk contribs 24,456 bytes +530 fixed error in the definition, in line with source. Made a better distinction between (generalized) eigenvectors and eigenvalues for (un)boudend SA operators undo

curprev 04:4704:47, 21 January 2024 Roffaduft talk contribs m 23,926 bytes −14 →Unbounded self-adjoint operators: minor grammatical fix undo

curprev 11:5611:56, 20 January 2024 Roffaduft talk contribs m 23,940 bytes +818 Changed subsection title "general SA operator" to "Unbounded SA operator" and included the notion of "generalized eigenvectors" to the subsection + reference. undo

curprev 06:2106:21, 17 December 2023 Citation bot talk contribs 23,122 bytes +31 Add: bibcode. | Use this bot. Report bugs. | Suggested by Whoop whoop pull up | Category:Linear algebra | #UCB_Category 21/287 undo

curprev 23:0623:06, 6 December 2023 2a02:1812:110c:dc00:4460:3cb2:f1db:1ee talk 23,091 bytes +12 No edit summary undo

curprev 10:0610:06, 16 October 2023 Dexxor talk contribs m 23,079 bytes −28 →Compact self-adjoint operators: linkfix undo

curprev 16:4916:49, 14 October 2023 65.183.138.55 talk 23,107 bytes +427 →Compact self-adjoint operators undo

curprev 00:1600:16, 30 September 2023 2601:200:c082:2ea0:1150:9bcd:9268:fc talk 22,680 bytes +25 →Hermitian maps and Hermitian matrices: can be identified with —> is equal to undo

curprev 08:2108:21, 27 September 2023 193.205.210.74 talk 22,655 bytes 0 →References undo

curprev 01:2801:28, 27 August 2023 2601:200:c082:2ea0:bc52:4192:d423:7e4c talk 22,655 bytes +13 →Finite-dimensional case undo

curprev 00:1600:16, 1 August 2023 103.90.35.214 talk 22,642 bytes −2 Undid revision 1168128288 by 103.90.35.214 (talk) undo Tag: Undo
curprev 00:1500:15, 1 August 2023 103.90.35.214 talk 22,644 bytes +2 →See also undo Tag: Reverted

curprev 15:2315:23, 22 July 2023 Hellacioussatyr talk contribs 22,642 bytes +34 →Bounded self-adjoint operators undo Tags: Mobile edit Mobile web edit Advanced mobile edit
curprev 15:1815:18, 22 July 2023 Hellacioussatyr talk contribs 22,608 bytes +129 →Finite-dimensional case: rm :-indents (MOS:INDENT); {{math theorem}} undo Tags: Mobile edit Mobile web edit Advanced mobile edit

curprev 13:5513:55, 29 November 2022 150.254.77.57 talk 22,479 bytes −9 →Multiplication operator version undo

curprev 12:0212:02, 17 November 2022 67.86.129.140 talk 22,488 bytes +18 →Hermitian maps and Hermitian matrices undo

curprev 22:5722:57, 2 November 2022 Mgkrupa talk contribs m 22,470 bytes −1 →References undo

curprev 20:4120:41, 18 March 2022 Chaoticgoodburger talk contribs m 22,471 bytes −434 Re-removed statement that U=V for SVD of normal matrices. This statement is indeed false. Note that Normal matrices are unitarily diagonalizable, but not necessarily orthogonally diagonalizable. As a counterexample take the sample normal matrix on that page where U does not equal V, diagonalizing that matrix requires complex eigenvectors while U and V are strictly real and orthogonal. Mandating that U=V is equivalent to A being Hermitian which much more specific than A being normal. undo Tag: Manual revert
curprev 05:5005:50, 18 March 2022 Jean Raimbault talk contribs 22,905 bytes +434 Undid revision 1077745741 by 2601:19B:700:CEF0:31A2:C7E5:2CC1:16FB (talk) the removed paragraph says nothing about eigenvalues of A itself undo Tags: Undo Reverted
curprev 00:3300:33, 18 March 2022 2601:19b:700:cef0:31a2:c7e5:2cc1:16fb talk 22,471 bytes −434 →Normal matrices: Removed a false statement — purely skew-symmetric matrices are normal though with complex eigenvalues, hence making the singular values and eigenvalues not equivalent. undo Tag: Reverted

curprev 18:4518:45, 9 February 2022 Qwerfjkl (bot) talk contribs m 22,905 bytes 0 Capitalising short description "result about when a matrix can be diagonalized" per WP:SDFORMAT (via Bandersnatch) undo

curprev 02:1402:14, 30 January 2022 Hellacioussatyr talk contribs 22,905 bytes +44 →Direct integrals undo Tags: Mobile edit Mobile web edit Advanced mobile edit
curprev 02:1102:11, 30 January 2022 Hellacioussatyr talk contribs 22,861 bytes +61 →Multiplication operator version undo Tags: Mobile edit Mobile web edit Advanced mobile edit

curprev 21:0521:05, 28 January 2022 Xinxtang talk contribs 22,800 bytes +434 →Normal matrices undo Tag: Visual edit

curprev 05:4405:44, 23 November 2021 LucasBrown talk contribs m 22,366 bytes +25 if-then undo

curprev 03:1903:19, 10 September 2021 Sepiabrown talk contribs 22,341 bytes −61 Made it clear the difference between spectral decompositon and eigendecompositon. undo
curprev 01:0101:01, 10 September 2021 Sepiabrown talk contribs 22,402 bytes −3 AFAIK, Augustin-Louis Cauchy proved the spectral theorem for symmetric matrices, not self-adjoint matrices undo

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