cometadata/datacite-titles-descriptions-related-identifiers huggingface dataset:
DOI: 10.6084/m9.figshare.30100678
title: Complex Eigenvalues, Orthogonality, and QR Factorization: Analytical Proofs and Numerical Verification

description: This research provides a rigorous investigation into complex eigenvalues and eigenvectors, inner products, and orthogonality in the context of Hermitian and normal matrices. The work includes both analytical proofs and numerical verification to ensure reproducibility and clarity.The methodology begins with a formal examination of Hermitian matrices, establishing that all eigenvalues are real and eigenvectors corresponding to distinct eigenvalues are orthogonal. These results are then validated through computational experiments using Python with the NumPy and SciPy libraries.Key computational techniques include:Eigenvalue and Eigenvector Computation: Generation of random Hermitian matrices and computation of their eigenvalues and eigenvectors. Orthogonality is verified numerically using absolute inner products, visualized through heatmaps.Gram–Schmidt Orthonormalization: Construction of orthonormal bases from linearly independent vectors. Reconstruction error and orthonormality error are computed and compared to SciPy’s QR decomposition to ensure numerical accuracy.QR Factorization and Least-Squares Solutions: QR decomposition is applied to overdetermined systems to solve least-squares problems. Discrepancies between QR-based solutions and NumPy’s lstsq method are quantified to confirm high accuracy (~10⁻¹⁶), demonstrating numerical stability and machine-precision correctness.All four figures referenced in this work are generated programmatically and saved in the eigenvalues/ folder, allowing full reproduction of results:Figure 1: Eigenvector orthogonality heatmapFigure 2: Gram–Schmidt vs SciPy QR reconstruction errorsFigure 3: Least-squares solution comparisonFigure 4: Gram–Schmidt vectors orthonormality heatmapNo human or animal data were used, and no ethical approval was required, as all computations are fully synthetic.This study provides a computationally verified, reproducible framework for exploring key concepts in numerical linear algebra, and it is suitable as both a teaching resource and a reference for researchers implementing high-precision matrix computations.
DOI: 10.6084/m9.figshare.30100678.v1
title: Complex Eigenvalues, Orthogonality, and QR Factorization: Analytical Proofs and Numerical Verification

description: This research provides a rigorous investigation into complex eigenvalues and eigenvectors, inner products, and orthogonality in the context of Hermitian and normal matrices. The work includes both analytical proofs and numerical verification to ensure reproducibility and clarity.The methodology begins with a formal examination of Hermitian matrices, establishing that all eigenvalues are real and eigenvectors corresponding to distinct eigenvalues are orthogonal. These results are then validated through computational experiments using Python with the NumPy and SciPy libraries.Key computational techniques include:Eigenvalue and Eigenvector Computation: Generation of random Hermitian matrices and computation of their eigenvalues and eigenvectors. Orthogonality is verified numerically using absolute inner products, visualized through heatmaps.Gram–Schmidt Orthonormalization: Construction of orthonormal bases from linearly independent vectors. Reconstruction error and orthonormality error are computed and compared to SciPy’s QR decomposition to ensure numerical accuracy.QR Factorization and Least-Squares Solutions: QR decomposition is applied to overdetermined systems to solve least-squares problems. Discrepancies between QR-based solutions and NumPy’s lstsq method are quantified to confirm high accuracy (~10⁻¹⁶), demonstrating numerical stability and machine-precision correctness.All four figures referenced in this work are generated programmatically and saved in the eigenvalues/ folder, allowing full reproduction of results:Figure 1: Eigenvector orthogonality heatmapFigure 2: Gram–Schmidt vs SciPy QR reconstruction errorsFigure 3: Least-squares solution comparisonFigure 4: Gram–Schmidt vectors orthonormality heatmapNo human or animal data were used, and no ethical approval was required, as all computations are fully synthetic.This study provides a computationally verified, reproducible framework for exploring key concepts in numerical linear algebra, and it is suitable as both a teaching resource and a reference for researchers implementing high-precision matrix computations.
DOI: 10.15468/dl.7b2nke
title: Occurrence Download

description: A dataset containing 23960 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Calystegia silvatica",
 "Country is United Kingdom of Great Britain and Northern Ireland",
 "HasCoordinate is true"
 ]
}

 The dataset includes 23960 records from 80 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0051875-250827131500795/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.d877p2
title: Occurrence Download

description: A dataset containing 78332 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is one of (Australia)",
 "HasCoordinate is true",
 "Year is greater than or equal to 1957",
 "Year is less than or equal to 1957"
 ]
}

 The dataset includes 78332 records from 176 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0051844-250827131500795/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.zy7323
title: Occurrence Download

description: A dataset containing 851 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Calystegia silvatica",
 "Country is United States of America",
 "HasCoordinate is true"
 ]
}

 The dataset includes 851 records from 60 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0051877-250827131500795/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.bn92dj
title: Occurrence Download

description: A dataset containing 0 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is incertae sedis",
 "Year is greater than 2013",
 "Geometry MULTIPOLYGON (((18.331109 40.371052,18.331636 40.370611,18.331964 40.370218,18.332392 40.370019,18.332451 40.369757,18.333076 40.369084,18.334107 40.36823,18.334266 40.367998,18.334462 40.367689,18.335439 40.367133,18.336315 40.366549,18.337538 40.366046,18.338271 40.365803,18.338582 40.365631,18.339374 40.365127,18.340802 40.364717,18.34205 40.364396,18.342588 40.364132,18.343402 40.363443,18.344169 40.362758,18.345108 40.362278,18.345837 40.361669,18.346826 40.360856,18.348013 40.3601,18.349517 40.359208,18.351064 40.358275,18.351327 40.358107,18.35255 40.357605,18.353011 40.357127,18.353601 40.356896,18.354629 40.356372,18.354851 40.356244,18.354821 40.356027,18.355132 40.355855,18.355438 40.355647,18.355513 40.355494,18.355494 40.35502,18.355601 40.354754,18.356081 40.354422,18.356208 40.354302,18.356305 40.353964,18.356461 40.353365,18.357332 40.352745,18.359512 40.351211,18.360573 40.350575,18.360974 40.350359,18.361165 40.350014,18.36173 40.349601,18.363186 40.348713,18.364098 40.348382,18.364478 40.348021,18.364784 40.347813,18.365109 40.347054,18.365965 40.346325,18.366156 40.345979,18.36639 40.345594,18.369162 40.343499,18.369525 40.343359,18.370063 40.343095,18.370241 40.342312,18.370693 40.341432,18.371171 40.340404,18.371975 40.339642,18.372477 40.339125,18.373358 40.338576,18.373828 40.338172,18.374014 40.33779,18.374295 40.337401,18.374459 40.337204,18.367738 40.335702,18.36645 40.33676,18.365599 40.337526,18.360532 40.341017,18.360184 40.341265,18.359805 40.341296,18.356776 40.340518,18.356046 40.340431,18.350214 40.344277,18.349935 40.344336,18.348182 40.343783,18.346927 40.343373,18.346606 40.343472,18.342458 40.346009,18.342459 40.346016,18.337519 40.349049,18.337217 40.350319,18.336308 40.351016,18.335961 40.35196,18.332449 40.352539,18.331949 40.352726,18.331634 40.353025,18.331119 40.354333,18.330814 40.355933,18.330549 40.356431,18.327182 40.359086,18.326966 40.35925,18.326734 40.361027,18.326493 40.361707,18.325517 40.363984,18.323692 40.365671,18.32347 40.365799,18.321713 40.368323,18.320305 40.370599,18.318833 40.3731,18.318502 40.375545,18.318047 40.376059,18.317591 40.376572,18.319287 40.377057,18.319752 40.37592,18.320392 40.375355,18.322308 40.37432,18.324344 40.373458,18.326975 40.372401,18.328408 40.372028,18.329246 40.37185,18.329572 40.371787,18.33011 40.371523,18.331109 40.371052)))"
 ]
}

 The dataset includes 0 records from 0 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0032685-230530130749713/datasets/export for details.
DOI: 10.25549/pcra-c14-16989
title: Minute book no. 7, PMU, AoG GB, HRMC, July 1927 - Dec. 1929

description: [description english/roman)] Pentecostal Missionary Union [PMU]/Assemblies of God [AoG] Home Reference Missionary Council [HRMC] minute Book No.7, including Home Reference Missionary Council annual statement, 32 pages of index followed by 165 pages of minutes relating to missionaries and ends with 2 pages of accounts. All matters relating to Assemblies of God [AoG] Home Reference Missionary Council council member appointments, decisions, policy and missionary personnel issues.
DOI: 10.15468/dl.w3kdbg
title: Occurrence Download

description: A dataset containing 5168 species occurrences available in GBIF matching the query:
{
 "and" : [
 "CoordinateUncertaintyInMeters 0.0-28.0",
 "Country is Germany",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "IucnRedListCategory is one of (CR, EN, VU, NT)",
 "MediaType is Image",
 "OccurrenceStatus is Present",
 "Year 2016-2022"
 ]
}

 The dataset includes 5168 records from 5 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0147443-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.wdvdzz
title: Occurrence Download

description: A dataset containing 104891 species occurrences available in GBIF matching the query:
{
 "and" : [
 "BasisOfRecord is Human Observation",
 "Country is Norway",
 "DatasetKey is Norwegian breeding bird monitoring scheme",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "Year 1980-2023"
 ]
}

 The dataset includes 104891 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0017338-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.25549/pcra-c14-16965
title: Minute book no. 7, PMU, AoG GB, HRMC, July 1927 - Dec. 1929

description: [description english/roman)] Pentecostal Missionary Union [PMU]/Assemblies of God [AoG] Home Reference Missionary Council [HRMC] minute Book No.7, including Home Reference Missionary Council annual statement, 32 pages of index followed by 165 pages of minutes relating to missionaries and ends with 2 pages of accounts. All matters relating to Assemblies of God [AoG] Home Reference Missionary Council council member appointments, decisions, policy and missionary personnel issues.
DOI: 10.15468/dl.7uz2nm
title: Occurrence Download

description: A dataset containing 536 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Eremanthus incanus (Less.) Less."
 ]
}

 The dataset includes 536 records from 50 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0015987-200613084148143/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.25549/pcra-c14-18631
title: Minute book no. 14, PMU, AoG GB, HRMC, May 1946 - Mar. 1948

description: [description english/roman)] Assemblies of God [AoG] OMC, Home Reference Missionary Council [HRMC] minute book No. 14 including OMC annual statement, 57 pages of index followed by 203 pages of minutes. All matters relating to AOG OMC council member appointments, decisions, policy and missionary personnel issues.
DOI: 10.15468/dl.chjp5p
title: Occurrence Download

description: A dataset containing 1536 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Rapistrum perenne (L.) All."
 ]
}

 The dataset includes 1536 records from 111 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0156009-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.t6cx7a
title: Occurrence Download

description: A dataset containing 689 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Pedersenia pulverulenta (Mart.) Holub"
 ]
}

 The dataset includes 689 records from 83 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0017319-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.25549/pcra-c14-18605
title: Minute book no. 14, PMU, AoG GB, HRMC, May 1946 - Mar. 1948

description: [description english/roman)] Assemblies of God [AoG] OMC, Home Reference Missionary Council [HRMC] minute book No. 14 including OMC annual statement, 57 pages of index followed by 203 pages of minutes. All matters relating to AOG OMC council member appointments, decisions, policy and missionary personnel issues.
DOI: 10.15468/dl.cfb5bi
title: Occurrence Download

description: A dataset containing 624 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Equus occidentalis (Leidy, 1865)"
 ]
}

 The dataset includes 624 records from 10 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0005277-180131172636756/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.2g5emr
title: Occurrence Download

description: A dataset containing 8 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Dicliptera gillilandiorum (K.Balkwill) I.Darbysh."
 ]
}

 The dataset includes 8 records from 3 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0070112-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.a8e44c
title: Occurrence Download

description: A dataset containing 7776 species occurrences available in GBIF matching the query:
{
 "and" : [
 "TaxonKey is Linum lewisii Pursh",
 "HasCoordinate is true"
 ]
}

 The dataset includes 7776 records from 142 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0039620-231120084113126/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.25549/pcra-c14-18599
title: Minute book no. 14, PMU, AoG GB, HRMC, May 1946 - Mar. 1948

description: [description english/roman)] Assemblies of God [AoG] OMC, Home Reference Missionary Council [HRMC] minute book No. 14 including OMC annual statement, 57 pages of index followed by 203 pages of minutes. All matters relating to AOG OMC council member appointments, decisions, policy and missionary personnel issues.
DOI: 10.15468/dl.2b4jwr
title: Occurrence Download

description: A dataset containing 426 species occurrences available in GBIF matching the query:
{
 "and" : [
 "HasCoordinate is true",
 "TaxonKey is Passiflora rubra L.",
 "HasGeospatialIssue is false"
 ]
}

 The dataset includes 426 records from 35 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0005277-180508205500799/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.25549/pcra-c14-18641
title: Minute book no. 14, PMU, AoG GB, HRMC, May 1946 - Mar. 1948

description: [description english/roman)] Assemblies of God [AoG] OMC, Home Reference Missionary Council [HRMC] minute book No. 14 including OMC annual statement, 57 pages of index followed by 203 pages of minutes. All matters relating to AOG OMC council member appointments, decisions, policy and missionary personnel issues.
DOI: 10.15468/dl.phr8ak
title: Occurrence Download

description: A dataset containing 138 species occurrences available in GBIF matching the query:
{
 "and" : [
 "GadmGid is BEL",
 "OccurrenceStatus is Present",
 "TaxonKey is Oxalis latifolia Kunth"
 ]
}

 The dataset includes 138 records from 5 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0156030-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.qs6b2n
title: Occurrence Download

description: A dataset containing 1 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Dicliptera tianmuensis (H.S.Lo)"
 ]
}

 The dataset includes 1 records from 1 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0070120-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.25549/pcra-c14-18644
title: Minute book no. 14, PMU, AoG GB, HRMC, May 1946 - Mar. 1948

description: [description english/roman)] Assemblies of God [AoG] OMC, Home Reference Missionary Council [HRMC] minute book No. 14 including OMC annual statement, 57 pages of index followed by 203 pages of minutes. All matters relating to AOG OMC council member appointments, decisions, policy and missionary personnel issues.
DOI: 10.15468/dl.4wdxha
title: Occurrence Download

description: A dataset containing 22 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Vella anremerica (Litard. & Maire) Gómez-Campo"
 ]
}

 The dataset includes 22 records from 16 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0155978-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.ny4ajb
title: Occurrence Download

description: A dataset containing 17 species occurrences available in GBIF matching the query:
{
 "TaxonKey" : [
 "is Dicliptera yunnanensis (W.W.Sm.)"
 ]
}

 The dataset includes 17 records from 7 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0070123-230530130749713/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.pzvrv3
title: Occurrence Download

description: A dataset listing the 4367 species recorded in GBIF matching the query:
{
 "and" : [
 "BasisOfRecord is Specimen",
 "Country is Brazil",
 "TaxonKey is Elasmobranchii"
 ]
}

 The dataset's 4367 records were derived from 55 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0005277-190320150433242/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.25549/pcra-c14-17822
title: Minute book no. 13, PMU, AoG GB, OMC, Sept. 1943-1946

description: [description english/roman)] Assemblies of God [AoG] Home Reference Missionary Council minute Book No. 13 including Home Reference Missionary Council annual statement, 61 pages of index followed by 207 pages of minutes. All matters relating to Assemblies of God [AoG] Home Reference Missionary Council council member appointments, decisions, policy and missionary personnel issues.
DOI: 10.15468/dl.283k6n
title: Occurrence Download

description: A dataset containing 378 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is South Africa",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "OccurrenceStatus is Present",
 "TaxonKey is Cortaderia selloana (Schult. & Schult.f.) Asch. & Graebn."
 ]
}

 The dataset includes 378 records from 6 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0017310-230224095556074/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.15468/dl.hmvggm
title: Occurrence Download

description: A dataset containing 804 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is Netherlands",
 "HasCoordinate is true",
 "HasGeospatialIssue is false",
 "TaxonKey is Plebejus argus (Linnaeus, 1758)",
 "Year 1970-2000"
 ]
}

 The dataset includes 804 records from 4 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0163917-220831081235567/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.25549/pcra-c14-242887
title: Programme for the dedication of the Lott & Crouch building, COGIC Mission School, Tugbake, Liberia, 1965

description: [description english/roman)] Programme for the dedication of the Lott & Crouch building, Church of God in Christ Mission School, Tugbake, Cape Palmas, Liberia, West Africa, 1965 August 15. Includes pages 2-6 of a more detailed program, plus another 2-page program.
DOI: 10.15468/dl.7t8qtj
title: Occurrence Download

description: A dataset containing 13 species occurrences available in GBIF matching the query:
{
 "and" : [
 "Country is Romania",
 {
 "or" : [
 "TaxonKey is Craspedacusta sowerbyi Lancaster",
 "TaxonKey is Girardia tigrina (Girard, 1850)",
 "TaxonKey is Dactylogyrus lamellatus Akhmerow, 1952",
 "TaxonKey is Heteronchocleidus buschkieli Bychowsky, 1957",
 "TaxonKey is Schyzocotyle acheilognathi (Yamaguti, 1934) Brabec, Waeschenbach, Scholz, Littlewood & Kuchta, 2015",
 "TaxonKey is Eudiplozoon nipponicum (Goto, 1891) Khotenovsky, 1984",
 "TaxonKey is Onchocleidus similis Mueller, 1936",
 "TaxonKey is Onchocleidus dispar Mueller, 1936",
 "TaxonKey is Hypania invalida (Grube, 1860)",
 "TaxonKey is Branchiura sowerbyi Beddard, 1892",
 "TaxonKey is Urnatella gracilis Leidy, 1851",
 "TaxonKey is Dreissena bugensis (Andrusov, 1897)",
 "TaxonKey is Dreissena polymorpha (Pallas, 1771)",
 "TaxonKey is Corbicula fluminea (O.F.Müller, 1774)",
 "TaxonKey is Corbicula fluminalis (O.F.Müller, 1774)",
 "TaxonKey is Sinanodonta woodiana (I.Lea, 1834)",
 "TaxonKey is Potamopyrgus antipodarum (J.E.Gray, 1843)",
 "TaxonKey is Ferrissia fragilis (Tryon, 1863)",
 "TaxonKey is Physella acuta (Draparnaud, 1805)",
 "TaxonKey is Planorbella anceps (Menke, 1830)",
 "TaxonKey is Pseudosuccinea columella (Say, 1817)",
 "TaxonKey is Cercopagis pengoi (Ostroumov, 1891)",
 "TaxonKey is Pacifastacus leniusculus (Dana, 1852)",
 "TaxonKey is Orconectes limosus (Rafinesque, 1817)",
 "TaxonKey is Procambarus fallax (Hagen, 1870)",
 "TaxonKey is Eriocheir sinensis H.Milne Edwards, 1853",
 "TaxonKey is Pectinatella magnifica (Leidy, 1851)",
 "TaxonKey is Aedes albopictus (Skuse, 1894)",
 "TaxonKey is Anopheles sacharovi Favre, 1903"
 ]
 }
 ]
}

 The dataset includes 13 records from 5 constituent datasets; see https://api.gbif.org/v1/occurrence/download/0022093-200613084148143/datasets/export for details.
 
Data from some individual datasets included in this download may be licensed under less restrictive terms.
DOI: 10.25549/pcra-c14-17844
title: Minute book no. 13, PMU, AoG GB, OMC, Sept. 1943-1946

description: [description english/roman)] Assemblies of God [AoG] Home Reference Missionary Council minute Book No. 13 including Home Reference Missionary Council annual statement, 61 pages of index followed by 207 pages of minutes. All matters relating to Assemblies of God [AoG] Home Reference Missionary Council council member appointments, decisions, policy and missionary personnel issues.