Mike's lecture on vector spaces and dual spaces: Revision history

25 June 2025

• curprev 14:4114:41, 25 June 2025 FloraC talk contribs m 17,108 bytes −124 Undo revision 203568 by VectorGraphics (talk). This is Mike's essay
• curprev 04:3004:30, 25 June 2025 VectorGraphics talk contribs 17,232 bytes +124 No edit summary Tag: Visual edit

31 March 2025

• curprev 15:4415:44, 31 March 2025 ArrowHead294 talk contribs m 17,108 bytes −6 No edit summary

11 November 2024

• curprev 16:3016:30, 11 November 2024 ArrowHead294 talk contribs m 17,114 bytes −10 →1.2: Covectors mean stuff. (OR: YOU DON'T KNOW MONZO)
• curprev 16:1916:19, 11 November 2024 ArrowHead294 talk contribs m 17,124 bytes −1 No edit summary
• curprev 16:1916:19, 11 November 2024 ArrowHead294 talk contribs m 17,125 bytes −256 Markup formatting

6 March 2023

• curprev 21:0721:07, 6 March 2023 Fredg999 talk contribs m 17,381 bytes +60 Categories
• curprev 21:0621:06, 6 March 2023 Fredg999 talk contribs m 17,321 bytes 0 Fredg999 moved page Mike's Lecture on Vector Spaces and Dual Spaces to Mike's lecture on vector spaces and dual spaces: WP:NCCAPS

5 January 2021

• curprev 11:2511:25, 5 January 2021 Inthar talk contribs m 17,321 bytes −31 →1.1: A monzo can be viewed as a VECTOR in a VECTOR SPACE[1].: idk if slight is the right word, since Z modules not necessarily being free is a big difference! Tags: Mobile edit Mobile web edit

7 December 2020

• curprev 04:3104:31, 7 December 2020 Inthar talk contribs m 17,352 bytes +31 /* 1.1: A monzo can be viewed as a VECTOR in a VECTOR SPACETechnically, monzos don't form a vector space but a "Z-module", because monzos only take integer coefficients and Z, the set of integers, is a ring but not a field. Similarly vals are a dual Z-module to the monzos. For practical purposes, this technicality is completely accounted for by tools like the x31eq temperament finder --- it might tell you that your temperament is a "contorted" version of another temperament, and in temperamen...
• curprev 00:0200:02, 7 December 2020 Inthar talk contribs m 17,321 bytes +3 wording

6 December 2020

• curprev 23:5823:58, 6 December 2020 Inthar talk contribs m 17,318 bytes +159 No edit summary
• curprev 23:5223:52, 6 December 2020 Inthar talk contribs m 17,159 bytes +38 +link
• curprev 23:5023:50, 6 December 2020 Inthar talk contribs m 17,121 bytes −95 →1.1: A monzo can be viewed as a VECTOR in a VECTOR SPACETechnically, monzos don't form a vector space but a "Z-module", because monzos only take integer coefficients and Z, the set of integers, is a ring but not a field. Similarly vals are a dual Z-module to the monzos. For practical purposes, this technicality just means that we have to be careful not to temper out a power of a comma, or take a wedgie out of a contorted val like 24p in the 5-limit..
• curprev 23:5023:50, 6 December 2020 Inthar talk contribs m 17,216 bytes −132 No edit summary
• curprev 23:4523:45, 6 December 2020 Inthar talk contribs m 17,348 bytes −152 format footnotes
• curprev 23:4023:40, 6 December 2020 Inthar talk contribs m 17,500 bytes +43 →1.3: Why the fact that covectors mean stuff matters. (OR: PREPARE FOR WEDGIE)
• curprev 23:3923:39, 6 December 2020 Inthar talk contribs m 17,457 bytes +48 →1.3: Why the fact that covectors mean stuff matters. (OR: PREPARE FOR WEDGIE)
• curprev 23:3723:37, 6 December 2020 Inthar talk contribs m 17,409 bytes +453 add note on vector spaces vs modules
• curprev 23:2923:29, 6 December 2020 Inthar talk contribs m 16,956 bytes +24 →1.1: A monzo can be viewed as a VECTOR in a VECTOR SPACE.: technically monzos form a Z-module, not a vector space

7 December 2019

• curprev 22:4822:48, 7 December 2019 000masa000 talk contribs m 16,932 bytes +13 →1.2: Covectors mean stuff. (OR: YOU DON'T KNOW MONZO)
• curprev 17:4317:43, 7 December 2019 000masa000 talk contribs 16,919 bytes +19 →EPISODE 1: Vector Spaces and Dual Spaces
• curprev 17:4217:42, 7 December 2019 000masa000 talk contribs 16,900 bytes −90 →EPISODE 1: Vector Spaces and Dual Spaces
• curprev 17:3917:39, 7 December 2019 000masa000 talk contribs 16,990 bytes +72 →EPISODE 1: Vector Spaces and Dual Spaces
• curprev 17:2617:26, 7 December 2019 000masa000 talk contribs m 16,918 bytes −64 plural of generator to match grammar Tag: Visual edit

31 July 2019

• curprev 06:2706:27, 31 July 2019 Mike Battaglia talk contribs 16,982 bytes −310 formatting

30 September 2018

• curprev 17:5117:51, 30 September 2018 Mike Battaglia talk contribs 17,292 bytes −3 formatting
• curprev 17:5117:51, 30 September 2018 Mike Battaglia talk contribs 17,295 bytes +9 change $$ to math tag

17 July 2018

• curprev 00:0000:00, 17 July 2018 Wikispaces>FREEZE 17,286 bytes +17,286 No edit summary

10 March 2013

• curprev 11:1011:10, 10 March 2013 Wikispaces>Ninly 46,022 bytes +46,022 **Imported revision 413577762 - Original comment: Reverted to May 9, 2012 9:44 am: reverting typo fix, script glitch broke page**
• curprev 11:0711:07, 10 March 2013 Wikispaces>Ninly 91,667 bytes +91,667 **Imported revision 413577316 - Original comment: typo in val toward end of sec. 1.2: <12 19 18|**

9 May 2012

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27 April 2012

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