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Smith normal form

normal form for a matrix with values in a principal ideal domain
Thing canonical_form Q7545384
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Smith normal form

Summary

Smith normal form is a canonical form[1]. It draws 122 Wikipedia views per month (canonical_form category, ranking #3 of 12).[2]

Key Facts

  • Smith normal form's instance of is recorded as canonical form[3].
  • Smith normal form's instance of is recorded as mathematical concept[4].
  • Smith normal form is a type of matrix[5].
  • Smith normal form's different from is recorded as structure theorem for finitely generated modules over a principal ideal domain[6].
  • Smith normal form's maintained by WikiProject is recorded as WikiProject Mathematics[7].

Body

Definition and Type

Recorded instance of include canonical form[3] and mathematical concept[4]. Smith normal form is a type of matrix[5].

Why It Matters

Smith normal form draws 122 Wikipedia views per month (canonical_form category, ranking #3 of 12).[2] It has Wikipedia articles in 6 language editions, a strong signal of global cultural recognition.[8]

References

Programmatic citations — every numbered marker resolves to a verifiable graph row below.

Direct Wikidata claims

  1. [3] ↑ . wikidata.org.
  2. [4] ↑ . wikidata.org.
  3. [5] ↑ . wikidata.org.
  4. [6] ↑ . wikidata.org.
  5. [7] ↑ . wikidata.org.

Class ancestry

  1. [1] ↑ . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] ↑ . Wikimedia Foundation. dumps.wikimedia.org.
  2. [8] ↑ . Wikidata sitelinks. wikidata.org.

📑 Cite this page

Use these citations when quoting this entity in research, articles, AI prompts, or wherever provenance matters. We aggregate Wikidata + Wikipedia + authoritative open-data sources; the stitched, scored, cross-referenced view is what 4ort.xyz contributes.

APA 4ort.xyz Knowledge Graph. (2026). Smith normal form. Retrieved May 3, 2026, from https://4ort.xyz/entity/smith-normal-form
MLA “Smith normal form.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/smith-normal-form.
BibTeX @misc{4ortxyz_smith-normal-form_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Smith normal form}}, year = {2026}, url = {https://4ort.xyz/entity/smith-normal-form}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Smith normal form — https://4ort.xyz/entity/smith-normal-form (retrieved 2026-05-03)

Canonical URL: https://4ort.xyz/entity/smith-normal-form · Last refreshed:

Edit History

Rolling log of changes to this entity's Wikidata record. Values shown reflect the current state of each edited property — follow the history link to see the precise diff for any edit.

  1. 7h ago · Charp238 · 2026-05-21 view diff on Wikidata ↗
    Subclass of → matrix
    Maintained by wikiproject → WikiProject Mathematics
    Different from → structure theorem for finitely generated modules over a principal ideal domain
    Defining formula → \operatorname{diag}(\alpha_1,\dotsc,\alpha_r,0,\dotsc,0)\qquad(\alpha_1\mid\alph
    + 5 other properties edited (see Wikidata diff for full list)
    "/* wbsetclaim-create:2||1 */ [[Property:P2534]]: \operatorname{diag}(\alpha_1,\dotsc,\alpha_r,0,\dotsc,0)\qquad(\alpha_1\mid\alpha_2\mid\dotsb\mid\alpha_r)"
Live feed via Wikidata EventStreams. New edits appear within minutes of being made on Wikidata.