hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Reducing subspace
In linear algebra, a reducing subspace  of a linear map  from a Hilbert space  to itself is an invariant subspace of  whose orthogonal complement  is also an invariant subspace of  That is,  and  One says that the subspace  reduces the map

One says that a linear map is reducible if it has a nontrivial reducing subspace. Otherwise one says it is irreducible.

If  is of finite dimension  and  is a reducing subspace of the map  represented under basis  by matrix  then  can be expressed as the sum

where  is the matrix of the orthogonal projection from  to  and  is the matrix of the projection onto   (Here  is the identity matrix.)

Furthermore,  has an orthonormal basis  with a subset that is an orthonormal basis of . If  is the transition matrix from  to  then with respect to  the matrix  representing  is a block-diagonal matrix

with  where , and

Projection (linear algebra)
In linear algebra and functional analysis, a projection is a linear transformation  from a vector space to itself (an endomorphism) such that . That is, whenever  is applied twice to any vector, it gives the same result as if it were applied once (i.e.  is idempotent). It leaves its image unchanged. This definition of "projection" formalizes and generalizes the idea of graphical projection.  One can also consider the effect of a projection on a geometrical object by examining the effect of the projection on points in the object.
Nayyar Hussain Bukhari
Nayyar Hussain Bukhari (Urdu: سید نیئر حسین بخاری; born 23 December 1952) is the senior leader of the Pakistan Peoples Party (PPP) who served as the 6th Chairman of the Senate of Pakistan, in office from 12 March 2012 to 12 March 2015.

A strong proponent of social democracy, he is also the key member of the Senate Standing Committee on Water and Power since 17 April 2009. Bukhari is currently a consultant to Lufthansa airlines in Frankfurt, Germany.

Chairman of the Senate of Pakistan
The chairman of the Senate of Pakistan (Urdu: صدر ایوانِ بالا, romanized: s̤adr-e Aiwān-e-Bālā) is the president-chair of the Senate of Pakistan. According to the Constitution of Pakistan, the chairman is a presiding official and the Senate must choose a chairman and deputy chairman for a time interval of three years.

During the president's absence, the chairman of the Senate is empowered with the duties of the presidency; in rare events involving the absence of the chairman, the presidential duties are usually held by the speaker of the National Assembly. The chairman of the Senate is the first in the line of succession to the president of Pakistan, ahead of the speaker of the National Assembly.

The first chairman of the Senate was Habibullah Marwat, while Wasim Sajjad remains the longest-serving chairman. Senator Yusuf Raza Gilani elected to Senate in the April 2 election, is the current chairman of the Senate, having assumed office on 9 April 2024.
Port Kells
Port Kells is a neighborhood of Guildford, a town center in Surrey, British Columbia. The neighborhood is located in the northeastern sector of Guildford, and is adjacent to the Fraser River and west of Walnut Grove, Langley. It has two major components: a large rural southern portion located south of Highway 1, and a section north of the highway that consists mostly of industrial parks.

Guildford, British Columbia
Guildford is a town centre and neighbourhood of Surrey, British Columbia, Canada. It is known for its retail corridors along 104 Avenue and 152 Street. At the intersection of these two streets sits the 200-store Guildford Town Centre shopping mall. The community is named after Guildford in Surrey, England.

Although Guildford is geographically large, the Guildford neighbourhood is locally considered to centre around the Guildford Town Centre mall and its surrounding blocks. A notable landmark in Guildford is the 86-metre (282 ft) tall flagpole, which had been located at the Expo 86 fairgrounds and was then the record holder for world's tallest flagpole. It is also home to the Guildford Recreation Centre, which is owned and operated by the City of Surrey to serve the recreational needs of local residents.

As of the 2016 census, the population of Guildford is 60,745.
Enzian (Bavarian Forest)
The Enzian is a mountain, 1,285 m above sea level (NHN), in the Bavarian Forest in Germany. It rises from the ridge northwest of the Arber and its summit lies on the boundary between the counties of Cham and Regen, with the municipality of Lohberg in the north and Drachselsried in the west-southwest.

The E6 European long distance path runs over its bare, flat summit from the Arber to the Kaitersberg. At the highest point is a checkpoint (Stempelstelle) and a summit register. On a walk along the crest of the Arber views open up time and again of the Zellertal valley and the bowl of the Lamer Winkel. However, the Enzian is almost never climbed as a destination on its own.

Cham (district)
Cham (German pronunciation: [kaːm] ⓘ) is a Landkreis (district) in Bavaria, Germany. It is bounded by (from the south and clockwise) the districts of Regen, Straubing-Bogen, Regensburg and Schwandorf and by the Czech Plzeň Region.
Tuzlaite
Tuzlaite is a borate mineral, associated with halides, named after the Tuzla salt mines in Bosnia and Hercegovina. A multitude of rare evaporate minerals have been discovered there, it being the only major evaporate deposit in the Balkans. This mineral has been approved as tuzlaite by the International Commission on New Minerals and Mineral Names.

Evaporite
An evaporite (/ɪˈvæpəˌraɪt/) is a water-soluble sedimentary mineral deposit caused by the concentration and crystallization (chemical precipitation) that results when enough of the water solvent evaporates from an aqueous solution. There are two types of evaporite deposits: marine, which can also be described as ocean deposits, and non-marine, which are found in standing bodies of water such as lakes. Evaporites are considered sedimentary rocks and are formed by chemical sediments.
Keith Gull
Professor Keith Gull CBE FRS FMedSci (born 29 May 1948) is a Wellcome Trust Principal Research Fellow and Professor of Molecular microbiology at the Sir William Dunn School of Pathology, University of Oxford.  He was the principal of St Edmund Hall, Oxford from 1 October 2009 to 30 September 2018, succeeding Michael Mingos.

Fellow of the Academy of Medical Sciences
Fellowship of the Academy of Medical Sciences (FMedSci) is an award for medical scientists who are judged by the UK Academy of Medical Sciences for the "excellence of their science, their contribution to medicine and society and the range of their achievements".
Russell Weir
Russell David Weir (11 July 1951 – 21 September 2022) was a Scottish professional golfer. He chose not to play on the main tours, remaining a club professional. He played mostly on the Scottish PGA circuit, the "Tartan Tour", where he won over 100 times. He won the PGA Club Professionals Championship in 1987 and 1988 and won the European club professional title three times. He played in eight consecutive PGA Cup matches between 1986 and 2000 and was captain of the Great Britain and Ireland team in 2011 and 2013. After reaching 50 he played on the European Senior Tour where he won once.

PGA Professional Championship (Great Britain and Ireland)
The PGA Professional Championship is a golf tournament run by The PGA for club professionals. It was first played in 1973 as the MacGregor PGA Club Professionals' Championship. The leading nine players in the event became the Great Britain and Ireland team for the first Diamondhead Cup, the forerunner of the PGA Cup, played against a United States team at Pinehurst later in the year.
Tiberiopolis
Tiberiopolis (Ancient Greek: Τιβεριούπολις; sometimes in sources, Tiberiapolis, and Pappa-Tiberiopolis; formerly Pappa) was a town in the Roman province of Phrygia Pacatiana, mentioned by Ptolemy, Socrates of Constantinople and Hierocles. At various times, it was considered as part of Phrygia, Isauria, and the late Roman province of Pisidia.

It struck its own coins at least from the time of Trajan.

It was situated at the modern village of Yunuslar, Beyşehir district, in Konya Province, Turkey. At Tiberiopolis the famous Roman sarcophagus showing the Twelve Labours of Hercules now displayed at the Konya Archaeological Museum was recovered.

It must have been Christianised at an early date. Nicephorus, a presbyter at Tiberiopolis was martyred in 361 or 362, and later canonized. His feast is celebrated on 28 November.

Beyşehir
Beyşehir (pronounced [ˈbejʃeˌhiɾ]) is a municipality and district of Konya Province, Turkey. Its area is 2,054 km2, and its population is 77,690 (2022). The town is located on the southeastern shore of Lake Beyşehir and is marked to the west and the southwest by the steep lines and forests of the Taurus Mountains, while a fertile plain, an extension of the lake area, extends in the southeastern direction.
Liam Millar
Liam Alan Millar (born September 27, 1999) is a Canadian professional soccer player who plays as an attacking midfielder or left winger for EFL Championship club Hull City and the Canada national team.

Millar featured in the youth ranks of Brampton Youth SC and North Mississauga SC before moving to England to join Fulham Academy aged 13. After three years with Fulham, he joined the Liverpool Academy in 2016.

2021–22 Swiss Cup
The 2021–22 Swiss Cup was the 97th season of Switzerland's annual football cup competition. The competition began on 13 August 2021 with the first games of Round 1. The final was held on 15 May 2022 at Wankdorf Stadium, Bern. Lugano defeated last year's runners-up St. Gallen 4–1 in the final to win their fourth Swiss Cup.

Luzern were the title holders.
Complete (The Smiths album)
Complete is a box set compilation by the English rock band the Smiths, released by Rhino Records on 26 September 2011. The standard CD and LP versions contain the band's four studio albums The Smiths (with "This Charming Man" added as per the original US release), Meat Is Murder, The Queen Is Dead and Strangeways, Here We Come, their only live album Rank and the three compilation albums released while the band were still active–Hatful of Hollow, The World Won't Listen and Louder Than Bombs–on eight CDs or eight LPs. A deluxe version contains those eight albums on both CD and LP formats, as well as 25 seven-inch vinyl singles and a DVD.

Rank (album)
Rank is the only official live album by the English band the Smiths. It was released in September 1988, a year after the band's breakup, through Rough Trade Records, and reached No. 2 in the British charts. In the USA, the album was released on Sire Records and made No. 77.
Kreis Goldap
The Goldap district was a Prussian district in East Prussia that existed from 1818 to 1945. Its territory is now divided between the Polish Warmian-Masurian Voivodeship and the Russian Kaliningrad Oblast.54°18′58″N 22°18′34″E﻿ / ﻿54.31611°N 22.30944°E﻿ / 54.31611; 22.30944

Suczki, Gołdap County
Suczki [ˈsut͡ʂki] is a village in the administrative district of Gmina Gołdap, within Gołdap County, Warmian-Masurian Voivodeship, in north-eastern Poland, close to the border with the Kaliningrad Oblast of Russia. It lies approximately 6 km (4 mi) south of Gołdap and 130 km (81 mi) north-east of the regional capital Olsztyn. It is located in the historic region of Masuria.

The village was founded by Poles.
Lok Fu
Lok Fu (Chinese: 樂富; Cantonese Yale: Lohk Fu) is a place in Wong Tai Sin District, Kowloon, Hong Kong. It is located to the east of Kowloon Tsai, the west of Wong Tai Sin and the north of Kowloon City. It geographically includes nearby Wang Tau Hom.

Morse Park
Morse Park (Chinese: 摩士公園), occupying 15.8 hectares (39 acres), is an urban park located in Wong Tai Sin in Kowloon.
It was completed in 1967. The park was named after Sir Arthur Morse (25 April 1892 – 13 May 1967), the head of The Hong Kong and Shanghai Banking Corporation during and after World War II.

City streets divide the park into four sections formally called Morse Park No. 1, Morse Park No. 2, and so on.
2014 FIVB Men's Volleyball World Championship qualification
The 2014 FIVB Men's Volleyball World Championship featured 24 teams. One place was allocated to the hosts, Poland, but no automatic place is given to the defending champions, Brazil. The remaining 23 places were determined by a qualification process, in which entrants from among the other teams from the five FIVB confederations competed.

2014 FIVB Men's Volleyball World Championship
The 2014 FIVB Men's Volleyball World Championship was held in Poland from 30 August to 21 September 2014. The tournament featured 24 teams to determine the world champions in men's volleyball. In addition to the host nation Poland, 23 teams qualified for the tournament through continental and regional competitions. The matches took place in seven venues across seven Polish cities, with the final being played at Spodek, Katowice.

The tournament was won by the hosts Poland, who beat Brazil (who had won the previous three titles) in the final. Poland became the third team in the history of the competition to be crowned as champions in their own country, joining the Soviet Union (1952 and 1962) and Czechoslovakia (1966).

563,263 fans watched the matches during the 18-day event, smashing the previous records in the competition. In Italy four years earlier, the total was 339,324, while in Japan in 2006, it was 298,352.
Geelvink Bay flying fox
The Geelvink Bay flying fox or Geelvink Bay fruit bat (Pteropus pohlei) is a species of flying fox in the family Pteropodidae. It is endemic to the islands of Yapen, Numfor, and Rani, which lie north of New Guinea in Indonesia's Papua Province. The name comes from Geelvink Bay, now Cenderawasih Bay.

It is common over a small area, and the population trend is decreasing.  Major threats to the species are loss of habitat due to timber harvesting, and hunting.

Numfor
Numfor (also Numfoor, Noemfoor, Noemfoer) is one of the Biak Islands (also known as the Schouten Islands) in Papua province, northeastern Indonesia.

It was the site of conflict between Japanese and the Allied forces during World War II, and was a major airbase for both sides.
John Carrick (cricketer)
John Carrick (29 November 1853 — 3 November 1916) was a Scottish first-class cricketer and stockbroker.

The son of John Carrick, the city architect for Glasgow, he was born in November 1853 at Glasgow and was educated at The Glasgow Academy. He later made a single appearance in first-class cricket for the Marylebone Cricket Club (MCC) against Nottinghamshire at Lord's in 1882. Batting twice in the match, he was dismissed in the MCC first innings for 10 runs by William Attewell, while in their second innings he was dismissed for 3 runs by Alfred Shaw. In addition to playing first-class cricket, Carrick also played club cricket in Scotland for the West of Scotland Cricket Club from 1884 to 1887. He was by profession a stockbroker. Carrick died suddenly in England at Eastbourne in November 1916. His brother was James Stewart Carrick, a rugby international who was also noted as a cricketer.

Alfred Shaw
Alfred Shaw (29 August 1842 – 16 January 1907) was a Victorian cricketer and rugby footballer, who bowled the first ball in Test cricket and was the first to take five wickets in a Test innings (5/35). He made two trips to North America and four to Australia, captaining the English cricket team in four Test matches on the all-professional tour of Australia in 1881/82, where his team lost and drew two each. He was also, along with James Lillywhite and Arthur Shrewsbury, co-promoter of the tour. He also organised the first British Isles rugby tour to Australasia in 1888.
Oldfield white-bellied rat
The Oldfield white-bellied rat or soft-furred Taiwan niviventer (Niviventer culturatus) is a species of rodent in the family Muridae. It is found only in Taiwan. It has also been considered a subspecies of Niviventer niviventer and included in Niviventer confucianus.

Chinese white-bellied rat
The Chinese white-bellied rat (Niviventer confucianus) is a species of rodent in the family Muridae. It is widely spread in China and also occurs in northern Myanmar, northwest Thailand, and northwest Vietnam. It might also occur in northern Laos.
Highland Championships
The Highland Championships (informally called the Scottish Highland Championships) was a men's and women's grass court tennis tournament first established in 1896 as part of the Atholl Hydropathic Open Lawn Tennis Tournament. Also known as the Bell's Highland Championships for sponsorship reasons (1974–1981).

The championships were first held at the Athole Hydropathic tennis courts, Pitlochry, Perthshire, Scotland. The tournament was staged annually as part of the ILTF Circuit until 1981.

Tennis Scotland
Tennis Scotland is the official governing body of tennis in Scotland. It was founded as the Scottish Lawn Tennis Association (SLTA) in 1895.  Tennis Scotland provides support to member clubs and organisations and promotes tennis participation and development. Tennis Scotland is also the governing body for padel in Scotland.
Konjsko, Sevnica
Konjsko (pronounced [ˈkoːnskɔ]; German: Roßbach) is a small settlement in the hills above the right bank of the Sava River south of Boštanj in the Municipality of Sevnica in central Slovenia. The area is part of the historical region of Lower Carniola. The municipality is now included in the Lower Sava Statistical Region.

Boštanj, Sevnica
Boštanj (pronounced [bɔˈʃtaːn] or [ˈboːʃtan]; in older sources also Gorenji Boštanj, German: Obersavenstein, Savenstein, Sowenstein, or Sawenstein) is a village in the Lower Sava Valley in southeastern Slovenia. It consists of a nucleated centre on two terraces on the right bank of the Sava River along the main road from Celje to Krško, and two hamlets, Puše and Redna, on the slopes of the nearby hills. It is the central settlement of the local community, the largest local community in the Municipality of Sevnica. The village has a post office, a fire station, a primary school, two shops, a gas station, two bars, a restaurant, and a cultural hall named the TVD Partizan Hall (Dom TVD Partizan). It is surrounded by fields and orchards.
Arthur Singe
Arthur Percy Singe (7 July 1898 — 5 January 1936) was a New Zealand rugby league player who represented the national side in 1925, becoming Kiwi number 179 in the process. Prior to this he played for the New Zealand Army rugby team in 1919 in Great Britain and South Africa following the end of World War I where he fought. When he returned to New Zealand he played for the Marist rugby club, and then the Marist rugby league club along with several representative sides in both codes.

Rugby Football League
The Rugby Football League (RFL) is the governing body for rugby league in England. Founded in 1895 as the Northern Rugby Football Union following 22 clubs resigning from the Rugby Football Union, it changed its name in 1922 to the Rugby Football League.

Based at Sportcity in Manchester, it is responsible for organising professional competitions and, in association with the British Amateur Rugby League Association (BARLA), the community game. It also provides match officials for every level as well as administering the England national team

The Rugby Football League has been a member of the International Rugby League (IRL) since 1948 and European Rugby League (ERL) since its foundation in 2003.
Capu Tafunatu
The Capu Tafunatu is a mountain in the department of Haute-Corse on the island of Corsica, France.
It rises to an altitude of 2,335 metres (7,661 ft) in the Niolo piève in the northwest of the island. 
Located in the Monte Cintu massif near the Paglia Orba, it rises southeast of Manso on the edge of the commune of Albertacce.

Capu Tafunatu literally means "perforated head".
The top of the mountain is pierced by an opening 55 metres (180 ft) wide by 16 metres (52 ft), making it the largest natural arch in France.

Paglia Orba
The Paglia Orba (pronounced /ˌpa.ʎa ˈɔːr.ba/) is a mountain peak in the Monte Cinto massif in Corsica. 
It rises to an altitude of 2,525 metres (8,284 ft), between the valleys of the Golo (in the Niolo) and the Cavicchia (in the Filosorma). 
Relatively isolated, this peak, notable for its characteristic tooth-shaped silhouette, dominates the Fango Valley and the west coast of the island.

Straddling the municipalities of Albertacce and Manso, Paglia Orba is the second highest peak of the central chain and the Filosorma, behind Punta Minuta at 2,556 metres (8,386 ft).
1965–66 SC Tasmania 1900 Berlin season
The 1965–66 season was SC Tasmania 1900 Berlin's first and only season in the Bundesliga, the top tier of German football. They finished 18th in the Bundesliga and were relegated to the Regionalliga Berlin, having set multiple Bundesliga records such as least points, fewest goals, most goals conceded and fewest wins. They were eliminated from the DFB-Pokal in the first round by 1. FC Köln.

Regionalliga Berlin
The Regionalliga Berlin was the second-highest level of the German football league system in the city of West-Berlin in Germany from 1963 until the formation of the 2. Bundesliga in 1974. It was by far the smallest of the five Regionalligas.
Rafael Medoff
Rafael Medoff (born c. 1959) is an American professor of Jewish history and the founding director of The David Wyman Institute for Holocaust Studies, which is based in Washington, D.C. and focuses on issues related to America's response to the Holocaust.

State University of New York at Purchase
Purchase College, officially the State University of New York at Purchase and also commonly referred to as SUNY Purchase, is a public liberal arts college in Purchase, New York. Established in 1967 by Governor Nelson Rockefeller, SUNY Purchase is one of 13 comprehensive colleges in the State University of New York (SUNY) system.
Nationell Idag
Nationell Idag (National Today) was an independent Swedish periodical founded in 2002 by the now defunct extreme right-wing political party National Democrats. As of 2014, the paper described its platform as based on the ideology of the Sweden Democrat party. It was 16 pages long and was released once a week, reaching around 1800 readers. At the end of 2012 the paper lost state subsidy which was granted to it in 2010. The editor as of 2014 was Patrik Ehn.

The content of the periodical was based on political nationalism, criticism of multiculturalism and the Swedish immigration policy, and features about nationalist organisations in other countries.

National Democrats (Sweden)
The National Democrats (Nationaldemokraterna, ND) were a political party in Sweden, formed by a radical faction of national board of the Sweden Democrats (SD) in October 2001 after they were expelled from the SD. The party described itself as a democratic nationalist and ethnopluralist party. The party disbanded on 23 April 2014.

In the 2002 general election the party received 9,248 votes, far below the 4% threshold necessary for parliamentary representation. In the 2006 general election, the party received 3,064 votes (0.06%); however, they had representation in two municipalities south of Stockholm. In the 2010 general election, the party received 1,141 votes (0.02%). The chairman of the party was Marc Abramsson.

On 2 February 2008, the old party logo consisting of a blue and yellow sail was replaced with an orange cloudberry flower.
Ushachy
Ushachy (Belarusian: Ушачы, romanized: Ušačy; Russian: Ушачи, romanized: Ushachi) is an urban-type settlement in Vitebsk Region, Belarus. It serves as the administrative center of Ushachy District. The settlement is located 101 kilometres (63 mi) west of Vitebsk. As of 2024, it has a population of 5,773.

Vitebsk
Vitebsk or Vitsyebsk is a city in north-eastern Belarus. It serves as the administrative center of Vitebsk Region and Vitebsk District, though it is administratively separated from the district. As of 2025, it has 358,927 inhabitants, making it the country's fourth-largest city. It is served by Vitebsk Vostochny Airport and Vitebsk Air Base.