hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Steinitz exchange lemma
The Steinitz exchange lemma is a theorem in linear algebra concerning bases, dimensionality of a vector space, stating that for any set smaller than a spanning set, there is a set of vectors in the spanning set but missing from the smaller set that can be added to the smaller set to make that set spanning as well.

It can be used, for example, to show that any two bases for a finite-dimensional vector space have the same number of elements. The result is named after the German mathematician Ernst Steinitz. The result is often called the Steinitz–Mac Lane exchange lemma, also recognizing the generalization
by Saunders Mac Lane
of Steinitz's lemma to matroids.

Basis (linear algebra)
In mathematics, a set B of elements of  a vector space V is called a basis (pl.: bases) if every element of V can be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called basis vectors.

Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B. In other words, a basis is a linearly independent spanning set.

A vector space can have several bases; however all the bases have the same number of elements, called the dimension of the vector space.

This article deals mainly with finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces.

Basis vectors find applications in the study of crystal structures and frames of reference.
Enfield Chase railway station
Enfield Chase railway station is located in Windmill Hill, Enfield, in the London Borough of Enfield, north London, 9 miles 9 chains (9.11 miles, 14.67 km) from London King's Cross on the Hertford Loop Line. It is in London fare zone 5.

London Borough of Enfield
The London Borough of Enfield (pronunciationⓘ) is a London borough in Greater London, England. The main communities in the borough are Edmonton, Enfield, Southgate and Palmers Green. Enfield is an Outer London borough and forms part of North London, being the northernmost borough and bordering Hertfordshire to the north and Essex to the northeast. The local authority is Enfield London Borough Council, based at Enfield Civic Centre. The borough's population is estimated to be 333,794.

It borders the London boroughs of Barnet to the west, Haringey to the south, and Waltham Forest to the southeast. To the north are the districts of Hertsmere, Welwyn Hatfield and Broxbourne (in Hertfordshire), and to the east is Epping Forest District in Essex.
Seven Regional WA
Seven Regional WA is an Australian television network serving all of Western Australia outside metropolitan Perth.  It launched on 10 March 1967 as BTW-3 in Bunbury, and became known as the Golden West Network (GWN, and later GWN7) in 1979. It serves one of the largest geographic television markets in the world—almost one-third of the continent.

In 2021, Prime Media Group merged with Seven and its independent branding was retired in 2022.

Viewer Access Satellite Television
The Viewer Access Satellite Television service, or VAST, is a satellite television platform in Australia, providing digital television and radio services to remote and rural areas, as well as viewers in terrestrial black spots. The service uses the Optus C1 and Optus D3 satellites. It is partly funded by the Australian Government and managed through a joint-venture between Seven West Media and Imparja Television. It is an even more restricted free-to-view replacement for Optus Aurora providing channels which have been absent (such as a Network Ten affiliate and digital only secondary and HD network channels) on the remote service until now. The platform uses only H.264 video encoding and 8PSK, which allows for more lower bit rate channels on the limited transponder space that's available. The EPG uses an MHEG-5 guide instead of the usual more compatible DVB EIT.
Foot Loose & Fancy Free
Foot Loose & Fancy Free is the eighth studio album by Rod Stewart, released in November 1977 on Riva Records in the UK and Warner Bros in the US.

The album is the second-to-last album of Stewart's 1970s albums, including the platinum-selling A Night on the Town. The album contains elements of hard rock ("Hot Legs"), funk rock ("You're Insane"), and progressive rock via Motown ("You Keep Me Hanging On"), as well as Stewart's usual ballads ("You're in My Heart"). "I Was Only Joking" was the third of four singles released from the album.

Hot Legs
"Hot Legs" is a single by Rod Stewart released in 1978 as the second single from his 1977 album Foot Loose & Fancy Free. The single performed moderately on the Billboard Hot 100, reaching number 28, but performed better on the UK Singles Chart, peaking at number 5. In the UK, "Hot Legs" and "I Was Only Joking" charted together as a double A-side.

In 1993, Stewart recorded a live version during his MTV Unplugged session which appeared on the album Unplugged...and Seated. Since the original recording, the lyrics in the last verse have been changed.

The lead guitar that is prominent throughout the song was performed by Billy Peek, a Saint Louis, Missouri native who was in Stewart's band in the mid-seventies.
Gabriel Teodros
Gabriel Teodros (born 1981) is a hip hop artist and a member of the groups Abyssinian Creole and CopperWire.  He was raised on Beacon Hill, Seattle, Washington. Teodros' music often features socially conscious themes, and he was a catalyst in the surge of dynamic underground rap acts from the Pacific Northwest during the first decade of the 2000s.

Common Market (hip-hop group)
Common Market is an American hip hop duo based in Seattle, Washington, active from 2005 through 2009 and from 2019 to present. Both members, DJ/Producer Sabzi (Saba Mohajerjasbi) and MC RA Scion (Ryan Abeo), had been active hip hop artists in the Pacific Northwest for three years before they combined their talents in 2005 to form Common Market. Together they have released two albums, three EPs, and have gone on several tours.
Steven Sykes
Steven Robert Sykes (born 5 August 1984 in Middelburg, Eastern Cape, South Africa) is a South African former rugby union player. He played for Oyonnax in the French Top 14. His regular position was lock.

Middelburg, Eastern Cape
Middelburg (Afrikaans pronunciation: [ˈmədəlbœrχ]) is a town in the Eastern Cape province of South Africa, in the Great Karoo. It lies in the Upper Karoo, 1,279 m above sea level, with a population of 19,000. It falls under the Inxuba Yethemba Local Municipality, in the Chris Hani District Municipality.
Muhammad Alwali II
Muhammad Dan Yaji,  known as Muhammad Alwali IIListenⓘ  (died 1807) was the last sultan of the Sultanate of Kano. His reign coincided with a period of upheavals in Sudanic History that saw a series of religious Jihads waged by the Fula People. In 1807, after a protracted struggle with Fula clans, Muhammad Alwali was ambushed and assassinated at Burum-Burum in modern Kano. His death marked the end of the Kutumbawa line of Hausa aristocrats in Kano and the fall of the 800 year old Bagauda Dynasty.

Bagauda dynasty
The Bagauda dynasty, also known as the Bagaudawa, is a house of noblemen who founded and ruled the kingdom (eventually sultanate) of Kano throughout its existence. The dynasty spanned over 800 years spread out through ten centuries, one of the longest in recorded human history and produced 43 rulers. After the fall of the dynasty in Kano, the remnants of the royal house founded a new kingdom in the Maradi Region.
Gertrude of Flanders, Countess of Savoy
Gertrude of Flanders (1135–1186) was a Countess Consort of Savoy by marriage to Humbert III, Count of Savoy.

She was the daughter of Thierry, Count of Flanders, and his second wife Sibylla of Anjou. In 1155, she married Humbert III, Count of Savoy, but he divorced and imprisoned her in 1163. She was freed thanks to Robert, bishop of Cambrai, and returned to the court of her brother, Philip of Flanders. She then returned to Flanders.

She remarried Hughues d'Oisy in 1168; the marriage was annulled in 1173, and she retired to a convent. She had no children. In 1177, she agreed to abstain for her right to Flanders in favor of her sister Margaret I, Countess of Flanders.

Thierry, Count of Flanders
Theoderic (Dutch: Diederik, French: Thierry, German: Dietrich; c. 1099 – 17 January 1168), commonly known as Thierry of Alsace, was the fifteenth count of Flanders from 1128 to 1168. With a record of four campaigns in the Levant and Africa (including participation in the Second Crusade, the failed 1157–1158 siege of the Syrian city Shaizar, and the 1164 invasion of Egypt), he had a rare and distinguished record of commitment to crusading.
Tooken
Tooken is a 2015 American parody film directed by John Asher and starring Lee Tergesen, Margaret Cho, Lauren Stamile and Laura-Leigh and features cameos by Ethan Suplee, Donnie Wahlberg, Akon, Michael Blackson and Jenny McCarthy. The film spoofs the action film genre, focusing mainly on the Taken series.

John Asher
John Mallory Asher (born John Mallory, January 13, 1971) is an American actor, film director, and screenwriter. He is perhaps best known for his performance as Gary on the USA Network's series spinoff of the movie Weird Science.
Greece men's national under-20 basketball team
The Greece men's national under-20 basketball team (Greek: Εθνική ομάδα καλαθοσφαίρισης Νέων Ανδρών Ελλάδας, (Greek young men's national basketball team) is the representative for Greece in international Under-20 age basketball competitions, and it is organized and run by the Hellenic Basketball Federation (E.O.K.). The Greece men's national under-20 basketball team represents Greece at the FIBA U20 EuroBasket. It was previously known as the Greek Under-22 national basketball team.

Hellenic Basketball Federation
The Hellenic Basketball Federation (abbreviated HBF; Greek: Ελληνική Ομοσπονδία Καλαθοσφαίρισης, abbreviated as Ε.Ο.Κ.,) is the main basketball governing body for the sport in Greece. It directs and oversees all of the national basketball teams of Greece, including both the junior and senior national teams, of both men and women. From 1969 to 1992, the E.O.K. also solely oversaw the top-tier level men's Greek National Basketball League, before its basic operation was taken over by HEBA, starting with the 1992–93 basketball season.
Hogar de los Tigres
Hogar de los Tigres (English: the Tigers' lair) is an indoor arena that is located in Sunchales, Santa Fe Province, Argentina. It is primarily used for basketball, and is the home arena of Libertad de Sunchales (nicknamed los Tigres). It holds 4,200 people.

Club Deportivo Libertad
Club Deportivo Libertad (usually called simply Libertad or Libertad de Sunchales) is a sports club from Argentina, with homebase in the Sunchales city of Santa Fe Province. The club is better known for both its association football and basketball teams.

Apart from those sports, other disciplines hosted by Libertad are bocce, equestrianism, karate, roller skating, tennis, and volleyball.
Francis McLean (engineer)
Sir Francis Charles McLean CBE (6 November 1904 – 19 December 1998) was a British electronics engineer. He was chief engineer of the Psychological Warfare Division of the Supreme Headquarters, Allied Expeditionary Force (PWD Shaef) in World War II, and Director of Engineering at the BBC from 1963 to 1968.

McLean was born in Ladywood, Birmingham, the eldest son of Michael and Alice McLean. He graduated from the University of Birmingham.

In 1966, he delivered a Faraday Lecture on the subject of colour television, in whose development he was instrumental. He was made a Knight Bachelor in 1967 and retired from the BBC in 1968. He chaired the Royal Commission on FM Broadcasting in Australia.

He appeared as a castaway on the BBC Radio programme Desert Island Discs on 12 August 1968.

A dormitory block at the BBC training centre at Wood Norton, Worcestershire, was named in his honour.

He died in West Berkshire.

FM broadcasting in Australia
FM broadcasting started in Australian capital cities in 1947 on an "experimental" basis, using a (monaural) ABC national network feed, consisting largely of classical music and Parliament, as a programme source. FM receivers were expensive and the audience consisted largely of hi-fi enthusiasts. The transmitters (operated by the PMG's Dept) were shut down in 1961, as much of the standard FM band (98–108 MHz) was reserved for TV channel 5 (102.25 video carrier).
John Binkley
John Emerson "Johne" Binkley (born February 4, 1953, in Fairbanks, Alaska) is a riverboat pilot, businessman and Republican politician from the U.S. state of Alaska.  Binkley served for one term apiece in the Alaska House of Representatives and the Alaska Senate during the mid and late 1980s, but is perhaps better known for his candidacy for governor of Alaska in the 2006 primary election.  In that election, he finished far behind Sarah Palin (who would go on to win the governorship), but also far ahead of one-term incumbent governor Frank Murkowski, by then deeply unpopular amongst Alaskans.

In 2017, the Anchorage Daily News was acquired by Binkley Co., a group run by John's son, Ryan Binkley.

Binkley was elected chair of the non-partisan Alaska Redistricting Board in 2020, following his appointment to the five-member board by Senate President Cathy Giessel.

Anchorage Daily News
The Anchorage Daily News is a newspaper published by the Binkley Co., and based in Anchorage, Alaska. It is the most widely read newspaper and news website (adn.com) in the state of Alaska. The newspaper is headquartered in Anchorage, with bureaus in Wasilla and Juneau.
Bring Us Together (album)
Bring Us Together is the third album by Danish pop band The Asteroids Galaxy Tour. The album was recorded at Viktoria Recording Studio, Copenhagen and was released on September 15, 2014, by Hot Bus Records.

The Asteroids Galaxy Tour
The Asteroids Galaxy Tour is a Danish pop band consisting of vocalist Mette Lindberg and songwriter/producer Lars Iversen, formed in 2007. When performing live, the band extends to a five-piece, featuring Mikkel Balster Dørig (guitar), Simon Littauer (MPC and keys), and Rasmus Littauer (drums).
Beatrice Wind Farm
The Beatrice Offshore Wind Farm now known as Beatrice Offshore Windfarm Ltd (BOWL) project, is an offshore wind farm close to the Beatrice oil field in the Moray Firth, part of the North Sea 13 km off the north east coast of Scotland.

Moray Firth
The Moray Firth (/ˈmʌri-/; Scottish Gaelic: An Cuan Moireach, Linne Mhoireibh or Caolas Mhoireibh) is a roughly triangular inlet (or firth) of the North Sea, north and east of Inverness, which is in the Highland council area of the north of Scotland.

It is the largest firth in Scotland, stretching from Duncansby Head (near John o' Groats) in the north, in the Highland council area, and Fraserburgh in the east, in the Aberdeenshire council area, to Inverness and the Beauly Firth in the west.

Therefore, three council areas have Moray Firth coastline: Highland to the west and north of the Moray Firth and Highland, Moray and Aberdeenshire to the south.  The firth has more than 500 miles (800 km) of coastline, much of which is cliff.
George Nostrand
George Thomas Nostrand  (January 25, 1924 – November 8, 1981) was an American professional basketball player.

A 6-foot-8-inch (2.03 m) power forward/center from High Point University (1941–1944) and the University of Wyoming (1944–1945), Nostrand played four seasons (1946–1950) in the National Basketball Association as a member of the Toronto Huskies, Cleveland Rebels, Providence Steamrollers, Boston Celtics, Tri-Cities Blackhawks, and Chicago Stags. He averaged 8.2 points per game in his professional career.

Nostrand is perhaps best known for appearing in a series of Canadian newspaper advertisements to promote the first National Basketball Association game, a November 1, 1946 contest between Nostrand's Toronto Huskies and the New York Knicks. The advertisements promised that anyone taller than Nostrand would receive free admission to the opening game.

Providence Steamrollers
The Providence Steamrollers were a Basketball Association of America team based in Providence, Rhode Island. As of 2025, the Steamrollers were the last professional sports franchise from one of the Big Four leagues to be based in Rhode Island.
Saccharin
Saccharin, also called saccharine, benzosulfimide, or E954, or used in saccharin sodium or saccharin calcium forms, is a non-nutritive artificial sweetener. Saccharin is a sultam that is about 500 times sweeter than sucrose, but has a bitter or metallic aftertaste, especially at high concentrations. It is used to sweeten products, such as drinks, candies, baked goods, tobacco products, excipients, and for masking the bitter taste of some medicines. It appears as white crystals and is odorless.

Aftertaste
Aftertaste is the taste intensity of a food or beverage that is perceived immediately after that food or beverage is removed from the mouth. The aftertastes of different foods and beverages can vary by intensity and over time, but the unifying feature of aftertaste is that it is perceived after a food or beverage is either swallowed or spat out. The neurobiological mechanisms of taste (and aftertaste) signal transduction from the taste receptors in the mouth to the brain have not yet been fully understood. However, the primary taste processing area located in the insula has been observed to be involved in aftertaste perception.
Lucy Doolan
Lucy Rose Doolan (born 11 December 1987) is a New Zealand former cricketer who played as an all-rounder, batting right-handed and bowling right-arm off break. She appeared in 40 One Day Internationals and 33 Twenty20 Internationals for New Zealand between 2008 and 2013. She played domestic cricket for Wellington Blaze, as well as stints for Essex, Nottinghamshire and South Australia. In March 2019, she announced her retirement from all forms of cricket.

Nottinghamshire Women cricket team
The Nottinghamshire Women's cricket team is the women's representative cricket team for the English historic county of Nottinghamshire. They play their home games at John Fretwell Sporting Complex, Nettleworth and are captained by Teresa Graves.  In 2019, they played in Division One of the final season of the Women's County Championship, and in 2021 won the East Midlands Group of the Women's Twenty20 Cup. They are partnered with the East Midlands regional side The Blaze.
Pescadero Creek
Pescadero Creek is a major stream in Santa Cruz and San Mateo counties in California, United States. At 26.6 miles (42.8 km), it is the longest stream in San Mateo County and flows all year from springs in the Santa Cruz Mountains. Its source is at 1,880 feet (570 m) above sea level on the western edge of Castle Rock State Park, with additional headwaters in Portola Redwoods State Park, and its course traverses Pescadero Creek County Park and San Mateo County Memorial Park before entering Pescadero Marsh Natural Preserve at Pescadero State Beach and thence to the Pacific Ocean 14.4 miles (23 km) south of Half Moon Bay.

Pescadero Creek County Park
Pescadero Creek Park, located near Loma Mar, San Mateo County, California, United States, is operated by the San Mateo County Department of Parks. The park complex of 8,020 acres (32.5 km2) also includes the neighboring Memorial, Sam McDonald and Heritage Grove parks. The park borders Portola Redwoods State Park with seamless trails, and connects to Big Basin Redwoods State Park via a trail easement across private lands.
Raleigh Township, Wake County, North Carolina
Raleigh Township (also designated Township 1) is one of twenty townships within Wake County, North Carolina, United States. As of the 2010 United States census, Raleigh Township had a population of 117,838, a 6.5% increase over 2000.

Raleigh Township, occupying 37.5 square miles (97.2 km2) in central Wake County, is almost completely occupied by portions of the city of Raleigh, including the city's downtown area. The township is, for the most part, bounded by the I-440 Raleigh Beltline.

Wake County, North Carolina
Wake County, officially the County of Wake, is a county located in the U.S. state of North Carolina. As of the 2020 census, its population was 1,129,410, making it North Carolina's most populous county. From July 2005 to July 2006, Wake County was the 9th-fastest growing county in the United States, with Cary and Raleigh being the 8th- and 15th-fastest growing communities, respectively.

Its county seat is Raleigh, which is also the state capital. Eleven other municipalities are in Wake County, the largest of which is the town of Cary, the third-most populous city of the Research Triangle region and the seventh-most populous municipality in North Carolina.

It is governed by the Wake County Board of Commissioners, coterminous with the Wake County Public School System, with law enforcement provided by the Wake County Sheriff's Department. It is also part of the wider Triangle J Council of Governments, which governs regional planning.
Jan Schwarz
Jan Schwarz (27 September 1958 – 10 November 2023) was a Czech theologian, a spiritual leader, journalist and writer. He was the seventh Patriarch of the Czechoslovak Hussite Church from 2001 to 2005.

In 2000, he had been assigned as the press spokesman and in 2001 as the head of the Church of the church. His rule was marked by serious rambling between rival factions some refusing his patriarchy and threatening the division of the church. In 2005, he appeared in front of the church's Episcopal Central Council where he tended his resignation from the patriarchate. He also announced his decision to join the Religious Society of Czech Unitarians. He was also engaged in journalistic and writer activities.

The ecclesiastical council appointed Bishop Mgr. Štěpán Klásek as an interim administrator to prepare for the election of a new patriarch of the church. On 23 September 2006, Tomáš Butta was elected, in the first round of voting with absolute majority as eighth Patriarch of the Church.

Czechoslovak Hussite Church
The Czechoslovak Hussite Church (Czech: Církev československá husitská, CČSH or CČH; Slovak: Cirkev československá husitská) is a Christian church that separated from the Catholic Church after World War I in Czechoslovakia.

Both the Czechoslovak Hussite Church and Moravian Church trace their tradition back to the Hussite reformers and acknowledge Jan Hus (John Huss) as their predecessor. It was well-supported by Czechoslovakia's first president, Tomáš Garrigue Masaryk, who himself belonged to the Evangelical Church of Czech Brethren.

The Czechoslovak Hussite Church describes itself as neo-Hussite.
1951 Preakness Stakes
The 1951 Preakness Stakes was the 76th running of the $110,245 Preakness Stakes horse race for three-year-old Thoroughbreds. The second leg of the U.S. Triple Crown series, the event took place on May 19, 1951. Owned by Isabel Dodge Sloane's Brookmeade Stable and ridden by future U.S. Racing Hall of Fame inductee, Eddie Arcaro, Bold easily won the race by seven lengths over runner-up Counterpoint. The race was run on a track rated fast in a final time of 1:56 2/5.

For jockey Arcaro, the win was a record fourth time he had won the race.

Counterpoint (horse)
Counterpoint (1948–1969) was an American ChampionThoroughbred racehorse. He was sired by 1943 U.S. Triple Crown champion Count Fleet and out of the racemare Jabot, a multiple stakes winner and Santa Anita Parktrack record setter against 13 of the premier stake racers in the United States.