Moore–Penrose inverse

given a matrix A, the unique matrix B such that ABA = A, BAB = B, and that AB and BA are both Hermitian
Intangible mathematical_concept Q43219517
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Moore–Penrose inverse

Summary

Moore–Penrose inverse is a mathematical concept[1]. It ranks in the top 5% of mathematical_concept entities by monthly Wikipedia readership (448 views/month).[2]

Key Facts

  • Moore–Penrose inverse is credited with the discovery of Eliakim Hastings Moore[3].
  • Moore–Penrose inverse's instance of is recorded as mathematical concept[4].
  • Eliakim Hastings Moore is named after Moore–Penrose inverse[5].
  • Roger Penrose is named after Moore–Penrose inverse[6].
  • Moore–Penrose inverse's subclass of is recorded as generalized inverse[7].
  • Moore–Penrose inverse's time of discovery or invention is recorded as +1920-00-00T00:00:00Z[8].
  • Moore–Penrose inverse's Freebase ID is recorded as /m/01wym8[9].
  • Moore–Penrose inverse's defining formula is recorded as \begin{aligned}AA^+A&=A \ A^+AA^+ &= A^+ \ (AA^+)^ & = AA^+ \ (A^+A)^ &= A^+A \end{aligned}[10].
  • Moore–Penrose inverse's MathWorld ID is recorded as Moore-PenroseMatrixInverse[11].
  • Moore–Penrose inverse's maintained by WikiProject is recorded as WikiProject Mathematics[12].
  • Moore–Penrose inverse's Microsoft Academic ID is recorded as 21556879[13].
  • Moore–Penrose inverse's PlanetMath ID is recorded as MoorePenroseGeneralizedInverse[14].
  • Moore–Penrose inverse's OpenAlex ID is recorded as C21556879[15].

Body

Works and Contributions

Moore–Penrose inverse is credited with the discovery of Eliakim Hastings Moore[3].

Why It Matters

Moore–Penrose inverse ranks in the top 5% of mathematical_concept entities by monthly Wikipedia readership (448 views/month).[2] It has Wikipedia articles in 9 language editions, a strong signal of global cultural recognition.[16] It is known by 8 alternative names across languages and contexts.[17]

References

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

Direct Wikidata claims

  1. [4] . wikidata.org.
  2. [3] . wikidata.org.
  3. [5] . wikidata.org.
  4. [6] . wikidata.org.
  5. [7] . wikidata.org.
  6. [8] . wikidata.org.
  7. [9] . wikidata.org.
  8. [10] . wikidata.org.
  9. [11] . wikidata.org.
  10. [12] . wikidata.org.
  11. [13] . wikidata.org.
  12. [14] . wikidata.org.
  13. [15] . OpenAlex. Retrieved . docs.openalex.org. Provenance: wikidata.org.

Class ancestry

  1. [1] . Wikidata. wikidata.org.

Aggregate / graph-position facts

  1. [2] . Wikimedia Foundation. dumps.wikimedia.org.
  2. [16] . Wikidata sitelinks. wikidata.org.
  3. [17] . Wikidata aliases. 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). Moore–Penrose inverse. Retrieved May 3, 2026, from https://4ort.xyz/entity/moore-penrose-inverse
MLA “Moore–Penrose inverse.” 4ort.xyz Knowledge Graph, 4ort.xyz, 3 May. 2026, https://4ort.xyz/entity/moore-penrose-inverse.
BibTeX @misc{4ortxyz_moore-penrose-inverse_2026, author = {{4ort.xyz Knowledge Graph}}, title = {{Moore–Penrose inverse}}, year = {2026}, url = {https://4ort.xyz/entity/moore-penrose-inverse}, note = {Accessed: 2026-05-03}}
LLM prompt According to 4ort.xyz Knowledge Graph (aggregator of Wikidata, Wikipedia, and authoritative open-data sources): Moore–Penrose inverse — https://4ort.xyz/entity/moore-penrose-inverse (retrieved 2026-05-03)

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