hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Square root of a 2 by 2 matrix
A square root of a 2×2 matrix M is another 2×2 matrix R such that M = R2, where R2 stands for the matrix product of R with itself.  In general, there can be zero, two, four, or even an infinitude of square-root matrices. In many cases, such a matrix R can be obtained by an explicit formula.

Square roots that are not the all-zeros matrix come in pairs: if R is a square root of M, then −R is also a square root of M, since (−R)(−R) = (−1)(−1)(RR) = R2 = M.A 2×2 matrix with two distinct nonzero eigenvalues has four square roots. A positive-definite matrix has precisely one positive-definite square root.

Matrix multiplication
In mathematics, specifically in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices A and B is denoted as AB.

Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering.
Computing matrix products is a central operation in all computational applications of linear algebra.
James Mundell
James Mundell (died 1762) was a Scottish educator. He founded and ran the exclusive Mr Mundell's school in the West Bow of Edinburgh, from 1735 to 1762.

He was uncle of Robert Mundell, rector of Wallace Hall, which adapted the teaching methods of Mundell's Edinburgh school.

Grassmarket
The Grassmarket is a historic market place, street and event space in the Old Town of Edinburgh, Scotland. In relation to the rest of the city it lies in a hollow, well below surrounding ground levels.
Construction battalion
A construction battalion is a kind of military battalion that is formally designated to engage in construction, and particularly in the building of structures for military use. Examples of construction battalions include:

Naval Mobile Construction Battalion, US Navy

Amphibious Construction Battalion, US Navy

371st Engineer Construction Battalion, US Army

No. 2 Construction Battalion, Canadian Expeditionary Force

Construction battalion (Soviet Union, Russia, Belarus)

Bau-Bataillon (Nazi Germany)
Luftwaffen-Bau-Bataillon
Litauische Bau-Bataillon
Ost-Bau-Pionier-Bataillon 559
Bau-Bataillon 87
Bau-Bataillon 121
Bau-Bataillon 306

371st Engineer Construction Battalion
371st Engineer Construction Battalion or 371st Engineer Battalion was activated as a Special Service Regiment in February 1944, as a unit in the United States Army. Later this unit was redesignated a General Service Regiment. The unit was formed at Camp Ellis, Illinois from some regular Army officers and enlisted men, trained in the United States, then shipped overseas early in World War II to Riverside Station, Liverpool, England. They were the vanguard of many others to follow, including infantry and armored troops. Their purpose was to build facilities in preparation for those to follow. After the Normandy Invasion, they followed the front lines constructing roads, railroad bridges, hospitals, and other infrastructure needed by the advancing Armies. Serving until the surrender by Germany, the unit was discharged from the military on 8 November 1945 and the service members returned home.
Arnold J. Cane
Arnold J. Cane (December 11, 1914 – September 10, 1968) was an American lawyer, jurist, and legislator.

Born in Ontonagon, Michigan, Cane attended to the public schools in Ontonagon. He then received his doctorate and law degrees from Marquette University. He then practiced law in Menasha, Wisconsin. He served on the Menasha Board of Education and as justice of the peace. Cane served in the Wisconsin State Assembly 1951–1959 was a Republican. In 1962, he was elected a Wisconsin Circuit Court judge serving until his death. Four months before he died, he sustained serious injuries in a car accident, when he was struck by a drunk driver. He died in Neenah, Wisconsin of a heart attack.

Neenah, Wisconsin
Neenah (/ˈniːnə/ NEE-nə) is a city in Winnebago County, Wisconsin, United States. It is situated on the banks of Lake Winnebago, Little Lake Butte des Morts, and the Fox River approximately 10 miles (16 km) northeast of Oshkosh and 40 miles (64 km) southwest of Green Bay. Neenah's population was 27,319 at the 2020 census.

Neenah is within the geographic boundaries of the Town of Neenah, but is politically independent. The city is the southwesternmost of the Fox Cities of northeast Wisconsin. It is a principal city of the Oshkosh–Neenah metropolitan statistical area, which consists of all of Winnebago County and had 171,730 residents in 2020. It is sometimes referred to as a twin city with Menasha, with which it shares Doty Island.
Bial
Bial (Portela e C.ª, S.A.) is a pharmaceutical company headquartered in São Mamede do Coronado, in Trofa, Porto district, Portugal. It was founded in 1924, being among the largest companies of its kind in Portugal. Its products are sold in pharmacies in more than 58 countries on 4 continents: Europe, America, Africa, and Asia.

Porto District
Porto ([ˈpoɾtu] ⓘ) is a district located on the north-west coast of Portugal. The district capital is the city of Porto, the second largest city in the country. It is bordered by the Aveiro and Viseu districts to the south, Braga district to the north and Vila Real district to the east.

Its area is 2,395 km2 (925 sq mi) and its population is 1,817,172. In 2017, the main legal foreign populations were from Brazil (9,442), China (2,475), Ukraine (2,160), Italy (1,273), Spain (1,189), Angola (1,118), and Cape Verde (1,040). These numbers exclude those who obtained Portuguese citizenship, which is regular among recent Portuguese Brazilians or Portuguese-Africans.
The Scarecrow (Hollywood Television Theatre)
The Scarecrow is a two-hour American television play that was broadcast on January 10, 1972, as part of the Hollywood Television Theatre series on PBS.  It was based on the classic Percy MacKaye play, The Scarecrow, which was in turn based on Nathaniel Hawthorne's short story, "Feathertop".

The cast included Pete Duel (his last role before his suicide in December 1971), Gene Wilder, Blythe Danner, Will Geer, Nina Foch, Joan Tompkins, Sian Barbara Allen and Norman Lloyd. Lewis Freedman was the producer, and Boris Sagal directed.

For her work on The Scarecrow, Jan Scott won a Primetime Emmy Award for Outstanding Achievement in Art Direction or Scenic Design For a Dramatic Program or Feature Length Film Made for Television, a Single Program of a Series or a Special Program.

The television production fell into the United States public domain immediately upon release, because at the time a copyright notice needed to be visibly shown in the film, which the editors failed to provide.

Pete Duel
Peter Ellstrom Deuel (February 24, 1940 – December 31, 1971), known professionally as Pete Duel, was an American stage, television, and film actor, who starred as outlaw Hannibal Heyes (alias Joshua Smith) in the television series Alias Smith and Jones.
Doctor's Harbour
Doctor's Harbour is a ghost town in Newfoundland and Labrador. It is located within Division No. 3, Fortune Bay.

Most services could not be provided in Doctor's Harbour due to its size. These services would be provided in the Town of Belleoram, across the bay.

Some still travel to the location because of its natural beauty as one of the "South Coast Fjords", a geographical region spanning from Hermitage Bay to Cape Ray.

In 1935, The community had a recorded population of 31 in the 1935 census.

Division No. 3, Newfoundland and Labrador
Division No. 3, Newfoundland and Labrador is a census division in the Canadian province of Newfoundland and Labrador, primarily comprising the South Coast of the island of Newfoundland, starting roughly 10km northwest of Channel-Port aux Basques and ending roughly 10km east of Rencontre East. Like all census divisions in Newfoundland and Labrador, but unlike the census divisions of some other provinces, the division exists only as a statistical division for census data, and is not a political entity.

In the Canada 2021 Census, the division had a population of 13,920 (down from 15,560 in 2016) and a land area of 19,912.67 square kilometres.
Ireland in the Eurovision Song Contest 2022
Ireland was represented at the Eurovision Song Contest 2022 in Turin, Italy with the song "That's Rich" performed by Brooke. The Irish broadcaster Raidió Teilifís Éireann (RTÉ) organised the national final Eurosong 2022 in order to select the Irish entry for the 2022 contest. Six songs faced the votes of an international jury, a studio jury and a public televote which ultimately resulted in the selection of the Irish Eurovision entry.

Ireland was drawn to compete in the second semi-final of the Eurovision Song Contest which took place on 12 May 2022. Performing during the show in position 10, "That's Rich" was not announced among the top 10 entries of the second semi-final and therefore did not qualify to compete in the final. It was later revealed that Ireland placed 15th out of the 18 participating countries in the semi-final with 47 points.

RTÉ One
RTÉ One is an Irish free-to-air flagship television service owned and operated by RTÉ. It is the most-popular and most-watched television channel in the country and was launched as Telefís Éireann on 31 December 1961, it was renamed RTÉ in 1966, and it was renamed as RTÉ 1 upon the launch of RTÉ2 in 1978.  It is funded partly by the government's licence fee; the remainder of the funding is provided by commercial advertising. Because RTÉ is funded partly by the licence fee it shows considerably fewer advertisements than most other channels available in Ireland and Northern Ireland.

RTÉ One is available to 98% of the Irish population in HD on the Saorview DTT service. It is also available in Northern Ireland via Saorview, Freeview, Sky, and cable provider Virgin Media. The channel is also available online through RTÉ Player.
Grade II* listed buildings in East Sussex
The county of East Sussex is divided into six districts. The districts of East Sussex are Hastings, Rother, Wealden, Eastbourne, Lewes, and Brighton & Hove.

As there are 348 Grade II* listed buildings in the county they have been split into separate lists for each district.

Grade II* listed buildings in Hastings

Grade II* listed buildings in Rother

Grade II* listed buildings in Wealden

Grade II* listed buildings in Eastbourne

Grade II* listed buildings in Lewes (district)

Grade II* listed buildings in Brighton and Hove

Rother District
Rother is a local government district in East Sussex, England. Its council is based in Bexhill-on-Sea. The district is named after the River Rother which flows within its boundaries.

The neighbouring districts are Wealden, Tunbridge Wells, Ashford, Folkestone and Hythe, and Hastings. Aside from its coast, Hastings is surrounded by Rother.
Electorates of the Australian states and territories
The lower houses of the parliaments of the states and territories of Australia are divided into electoral districts. Most electoral districts (except the Australian Capital Territory and Tasmania, which have multi-member electorates using a proportional voting method) send a single member to a state or territory's parliament using the preferential method of voting. The area of a state electoral district is dependent upon the Electoral Acts in the various states and vary in area between them. At present, there are 409 state electoral districts in Australia.

State electoral districts do not apply to the upper house, or legislative council, in those states that have one (New South Wales, South Australia, Tasmania, Victoria and Western Australia). In New South Wales and South Australia, MLCs represent the entire state, in Tasmania they represent single-member districts, and in Victoria and Western Australia they represent a region formed by grouping electoral districts together.

Electoral system of Australia
The electoral system used for the election of members of the Australian Parliament is governed primarily by the Commonwealth Electoral Act 1918. The system presently has a number of distinctive features including compulsory enrolment; compulsory voting; majority-preferential instant-runoff voting in single-member seats to elect the lower house, the House of Representatives; and the use of the single transferable vote proportional representation system to elect the upper house, the Senate.

The timing of elections is governed by the Constitution and political conventions. Generally, elections are held approximately every three years and are conducted by the independent Australian Electoral Commission (AEC).
Bull Buchanan
Barry Buchanan (born January 15, 1968) is an American professional wrestler. He is best known for his appearances with the World Wrestling Federation / Entertainment (WWF/WWE) under the ring names Recon, Bull Buchanan and B² and for his appearances with All Japan Pro Wrestling (AJPW) and Pro Wrestling Noah (NOAH) as Buchanan. Primarily a tag team wrestler, Buchanan is a former WWF World Tag Team Champion, All Asia Tag Team Champion, GHC Tag Team Champion and USWA World Tag Team Champion.

Smoky Mountain Wrestling
Smoky Mountain Wrestling was a professional wrestling promotion that held events in the Appalachian area of the United States from October 1991 to December 1995, when it was run by Jim Cornette. The promotion was based in Knoxville, Tennessee, with offices in Morristown, Tennessee.
Tanay Karnik
Tanay Karnik is an electrical engineer from Intel Corporation in Hillsboro, Oregon. He was named a Fellow of the Institute of Electrical and Electronics Engineers (IEEE) in 2014 for his contributions to error-tolerant circuits and near-load voltage regulators.

Voltage regulator
A voltage regulator is a system designed to automatically maintain a constant voltage. It may use a simple feed-forward design or may include negative feedback. It may use an electromechanical mechanism or electronic components. Depending on the design, it may be used to regulate one or more AC or DC voltages.

Electronic voltage regulators are found in devices such as computer power supplies where they stabilize the DC voltages used by the processor and other elements. In automobile alternators and central power station generator plants, voltage regulators control the output of the plant. In an electric power distribution system, voltage regulators may be installed at a substation or along distribution lines so that all customers receive steady voltage independent of how much power is drawn from the line.
Benedict Graves
Benedict Graves (born 10 November 1996) is an English cricketer. He made his first-class debut on 28 March 2017 for Durham MCCU against Gloucestershire as part of the Marylebone Cricket Club University fixtures.

Durham University Centre of Cricketing Excellence
Durham University Centre of Cricketing Excellence (Durham UCCE), known as Durham MCC University (Durham MCCU) from 2010 to 2020, is a cricket coaching centre based at Durham University in Durham, County Durham, England, and the name under which the Durham University Cricket Club (DUCC) first team plays.
Khin Ma Hnaung
Khin Ma Hnaung (Burmese: ခင်မနှောင်း, [kʰɪ̀ɴ ma̰ n̥áʊɴ]) was a queen consort of King Raza II of Arakan from 1599 to 1612. The queen was a daughter of King Nanda of Toungoo Dynasty and his chief consort Hanthawaddy Mibaya. She was taken to Mrauk-U, after her father surrendered to the joint forces of Raza II and Minye Thihathu II of Toungoo in 1599. At Mrauk-U, she was known as the Tanzaung Mibara (တန်ဆောင်း မိဖုရား, "Queen of the Royal Hall"). She was one of the Razagyi's most beloved consorts. It is said that the king was so focused on his queen that he used to forget his important state matters.

Mrauk U
Mrauk U (/məˈraʊuː, ˈmraʊuː/ ⓘ mə-ROW-oo, MROW-oo) is a town in northern Rakhine State, Myanmar. It is the capital of Mrauk-U Township, a subregion of the Mrauk-U District.

Mrauk U is culturally significant for the local Rakhine (Arakanese) people and is the location of many important archeological sites. From 1430 until 1785, it was the capital of the Mrauk U Kingdom, the largest and most powerful Rakhine kingdom in history.
Canariomys
Canariomys is an extinct genus of rodents (Old World rats and mice) that once existed on the islands of Tenerife and Gran Canaria, part of the Canary Islands, Spain. These giant rats could reach a weight of about 1 kg (2.2 lb). They were herbivores; their diet was based on plant materials, probably soft vegetables such as roots, ferns, and berries, but not grass. C. tamarani were considered herbivores, eating everything plant-like except grass with good digging skills. While C. bravoi were considered as a rat character, because of its large size, with an omnivorous diet with good climbing skills. They were one of two groups of rodents native to the archipelago, alongside the lava mouse (Malpaisomys insularis), which was native to Fuerteventura and Lanzarote.

Gran Canaria
Gran Canaria (UK: /ˌɡræn kəˈnɛəriə, -ˈnɑːr-/, US: /ˌɡrɑːn kəˈnɑːriə, -ˈnɛər-/; Spanish: [ɡɾaŋ kaˈnaɾja] ⓘ), also Grand Canary Island, is the third-largest and second-most-populous island of the Canary Islands, a Spanish archipelago off the Atlantic coast of Northwest Africa. As of 2023 the island had a population of 862,893 that constitutes approximately 40% of the population of the archipelago. Las Palmas de Gran Canaria, the capital of the island, is the largest city of the Canary Islands and the ninth-largest city of Spain.

Gran Canaria is located in the Atlantic Ocean in a region known as Macaronesia about 150 kilometres (93 mi) off the northwestern coast of Africa and about 1,350 km (840 mi) from Europe. With an area of 1,560 km2 (600 sq mi) and an altitude of 1,956 m (6,417 ft) at Morro de la Agujereada, Gran Canaria is the third largest island of the archipelago in both area and altitude. Gran Canaria is also the third most populated island in Spain.
Peter Scot
Peter Scot is a brand of Indian whisky, manufactured by Khoday India Limited (KIL), and launched in May 1968. It is a flagship brand of the company and is manufactured at their Bangalore facility. In Khoday Distilleries Limited vs. The Scotch Whisky Association and Others, Peter Warren, an employee of Khoday, told the Supreme Court of India that the brand name Peter Scot was made up using his father's first name, "Peter", and his nationality, "Scot". Another factor in choosing the name was due to the British explorer, Captain Scott, and his son Peter Scott. Although the name "Scott" is spelt with two t's, it is phonetically the same as the word Scot. The brand's main competitors are Pernod Ricard's Blenders Pride and United Spirits Limited's Royal Challenge.

United Spirits
United Spirits Limited is an Indian alcoholic beverages company, and the world's second-largest spirits company by volume. It is a subsidiary of Diageo, and headquartered at UB Tower in Bangalore, Karnataka. USL exports its products to over 37 countries.

According to the official website of the company, as of March 2013, USL has more than 140 liquor brands, of which 15 brands each sell more than one million cases annually while 3 brands each sell more than 10 million cases annually.
Oleksiejczuk
Oleksiejczuk is a Polish patronymic surname of Ukrainian origin derived from the Ukrainian given name Oleksiy and East Slavic patronymic suffix -chuk.  It may be transliterated as Oleksiejchuk. Variant: Aleksijczuk. Ukrainian-language counterparts: Oleksiychuk,  Aleksiychuk (Russianized). Notable people with the surname include:

Michał Oleksiejczuk (born 1995), Polish mixed martial artist

Michał Oleksiejczuk
Michał Oleksiejczuk (born February 22, 1995) is a Polish mixed martial artist. A professional since 2014, he was the former Thunderstrike Fight League Light heavyweight champion in Poland.  He currently competes in the middleweight division of the Ultimate Fighting Championship (UFC).
Carolla Digital
Carolla Digital (formerly ACE Broadcasting Network) is an American podcast network. The flagship program of the network is The Adam Carolla Show, which is released daily. The network also produces several other shows that are released on a weekly basis.

Bryan Bishop
Bryan Bishop, frequently referred to on podcasts as Bald Bryan, is an American radio personality and New York Times Best Selling author, best known for his career on The Adam Carolla Show podcast and its previous radio version.
2015 Indian Premier League final
The 2015 Indian Premier League final was a day/night Twenty20 cricket match between the Mumbai Indians and the Chennai Super Kings, played on 24 May 2015, at Eden Gardens, Kolkata. It was held to determine the winner of the 2015 season of the Indian Premier League, the annual professional Twenty20 tournament in India. It was the third time these two teams met in the final, having previously played each other in the 2010 and 2013 finals.

Mumbai defeated Chennai by 41 runs to win their second IPL title, playing in their third IPL final. Their previous IPL victory had come at the same venue against the same opposition in 2013. Chennai were playing their sixth IPL final, attempting to win their third title. Mumbai captain Rohit Sharma was awarded man of the match for his innings of 50. The final was sold out, with a final attendance of around 67,000 people.

Suresh Raina
Suresh Raina (pronunciationⓘ; born 27 November 1986) is an Indian former international cricketer. He played for the India national team and represented Uttar Pradesh in domestic cricket. He was an aggressive left-handed middle-order batsman and who occasionally bowled right-arm off-spin. Raina is the first Indian batsman to hit a century in all three formats of international cricket, and the first Indian to score a century in the T20 World Cup. He was a member of the Indian team that won the 2011 Cricket World Cup and the 2013 ICC Champions Trophy.
Children's culture
Children's culture includes children's cultural artifacts, children's media and literature, and the myths and discourses spun around the notion of childhood. Children's culture has been studied within academia in cultural studies, media studies, and literature departments. The interdisciplinary focus of childhood studies could also be considered in the paradigm of social theory concerning the study of children's culture.

Discourse
Discourse is a generalization of the notion of a conversation to any form of communication. Discourse is a major topic in social theory, with work spanning fields such as sociology, anthropology, continental philosophy, and discourse analysis. Following work by Michel Foucault, these fields view discourse as a system of thought, knowledge, or communication that constructs our world experience. Since control of discourse amounts to control of how the world is perceived, social theory often studies discourse as a window into power. Within theoretical linguistics, discourse is understood more narrowly as linguistic information exchange and was one of the major motivations for the framework of dynamic semantics. In these expressions, denotations are equated with their ability to update a discourse context.