hotchpotch/wikipedia-multilingual-ir-related-lead-pairs huggingface dataset:
Matrix polynomial
In mathematics, a matrix polynomial is a polynomial with square matrices as variables. Given an ordinary, scalar-valued polynomial

this polynomial evaluated at a matrix  is

where  is the identity matrix.

Note that  has the same dimension as .

A matrix polynomial equation is an equality between two matrix polynomials, which holds for the specific matrices in question.  A matrix polynomial identity is a matrix polynomial equation which holds for all matrices A in a specified matrix ring Mn(R).

Matrix polynomials are often demonstrated in undergraduate linear algebra classes due to their relevance in showcasing properties of linear transformations represented as matrices, most notably the Cayley–Hamilton theorem.

The determinant of a matrix polynomial with Hermitian positive-definite (semidefinite) coefficients is a polynomial with positive (nonnegative) coefficients.

Identity matrix
In linear algebra, the identity matrix of size  is the  square matrix with ones on the main diagonal and zeros elsewhere. It has unique properties, for example when the identity matrix represents a geometric transformation, the object remains unchanged by the transformation. In other contexts, it is analogous to multiplying by the number 1.
Manfred Schmid
Manfred Schmid (born 6 June 1944 in Liezen) is an Austrian former luger who competed from the mid-1960s to the late 1970s. Competing in four Winter Olympics, he won two medals at Grenoble in 1968 with a gold in the men's singles event and a silver in the men's doubles event.

Schmid also won seven medals at the FIL World Luge Championships with two gold (doubles: 1969, 1970), four silvers (singles: 1969, 1975; doubles: 1967, 1971), and one bronze (singles: 1978). He won five medals at the FIL European Luge Championships with two silvers (Men's singles: 1974, Men's doubles: 1971) and three bronzes (Men's singles: 1971, 1973; Men's doubles: 1970).

Schmid finished third in the overall Luge World Cup men's singles championship in 1977–78.

FIL European Luge Championships 1971
The FIL European Luge Championships 1971 took place in Imst, Austria for the second time after having previously hosted the championships in 1956. A record four countries won medals at these championships.
Stockholm Water Festival
The Stockholm Water Festival (Swedish: Stockholms vattenfestival) was an annual street festival held in Stockholm, Sweden, in August from 1991 to 1999. The festival featured many activities in central Stockholm, but was eventually cancelled after the 1999 festival due to lack of funds.

During the Stockholm Water Festival of 1993, a JAS 39 Gripen aircraft crashed at the island of Långholmen in central Stockholm during a display of the new aircraft. Despite the crash occurring near thousands of spectators, only one person on the ground was injured.

Street fair
A street fair celebrates the character of a neighborhood. As its name suggests, it is typically held on the main street of a neighborhood.

The principal component of street fairs are booths used to sell goods (particularly food) or convey information. Some include carnival rides and parades. Many have live music and dance demonstrations.

Fairs typically range no more than a few blocks long, although some fairs, such as the 9th Avenue International Food Festival in New York City and the Solano Stroll in Northern California, extend more than a mile. A fair only one block long is commonly called a block party.
Lithophragma heterophyllum
Lithophragma heterophyllum, commonly known as hillside woodland star, is a species of flowering plant in the saxifrage family found in the western United States. It is native to the coastal mountain ranges of California, where it can generally be found in shady habitat. It is a rhizomatous perennial herb growing erect or leaning with a slender naked flowering stem. The leaves are located on the lower part of the stem, each divided into rounded lobes. The stem bears 3 to 12 flowers, each in a cuplike calyx of red or green sepals. The five petals are white, up to 1.2 centimeters long, and usually divided into about three pointed lobes.

Saxifragaceae
Saxifragaceae is a family of herbaceous perennial flowering plants, within the core eudicot order Saxifragales. The taxonomy of the family has been greatly revised and the scope much reduced in the era of molecular phylogenetic analysis. The family is divided into ten clades, with about 640 known species in about 35 accepted genera. About half of these consist of a single species, but about 400 of the species are in the type genus Saxifraga. The family is predominantly distributed in the northern hemisphere, but also in the Andes in South America.
Newhard
Newhard is a surname. Notable people with the surname include:

Peter Newhard (1783–1860), American politician

Robert Newhard (1884–1945), American cinematographer

Scott Newhard (born 1951), American politician

Peter Newhard
Peter Newhard (July 26, 1783 – February 19, 1860) was an American politician from Pennsylvania who served as a Democratic member of the U.S. House of Representatives for Pennsylvania's 8th congressional district from 1839 to 1843.
Culture of San Diego
The culture of San Diego is influenced heavily by American and Mexican cultures due to its position as a border town, its large Hispanic population, and its history as part of Spanish America and Mexico. San Diego's longtime association with the U.S. military also contributes to its culture. Present-day culture includes many historical and tourist attractions, a thriving musical and theatrical scene, numerous notable special events, a varied cuisine, and a reputation as one of America's premier centers of craft brewing.

Border town
A border town is a town or city close to the boundary between two countries, states, or regions. Usually the term implies that the nearness to the border is one of the things the place is most famous for. With close proximities to a different country, diverse cultural traditions can have certain influence to the place. Border towns can have highly cosmopolitan communities, a feature they share with port cities, as traveling and trading often go through the town. They can also be flashpoints for international conflicts, especially when the two countries have territorial disputes.
Songs from Home (Doc Watson and Merle Watson album)
Songs from Home is the title of a recording by the American folk music and country blues artists Doc Watson and Merle Watson, released in 2002. It contains tracks from Watson's years on the Poppy and United Artists labels plus four previously unreleased tracks.

At the Grammy Awards of 1980 "Big Sandy/Leather Britches" won the Grammy Award for Best Country Instrumental Performance.

22nd Annual Grammy Awards
The 22nd Annual Grammy Awards were held on February 27, 1980, at Shrine Auditorium, Los Angeles, and were broadcast live on American television. They recognized accomplishments by musicians from the year 1979. This year was notable for being the first year to have a designated category for Rock music.

Album of the Year went to Phil Ramone and Billy Joel for 52nd Street, and Song of the Year went to Kenny Loggins and Michael McDonald for "What a Fool Believes".
Glutamate formimidoyltransferase
Glutamate formimidoyltransferase is a methyltransferase enzyme which uses tetrahydrofolate as part of histidine catabolism. It catalyses two reactions. In the first, N-formimidoyl-L-glutamate (from histidine) transfers its formimidoyl group to tetrahydrofolate.

Alternatively, the enzyme can catalyse the transfer of a formyl group from N-formyl-L-glutamic acid.

It is classified under EC 2.1.2.5 and in mammals is found as part of a bifunctional enzyme that also has formimidoyltetrahydrofolate cyclodeaminase activity.

Aldehyde
In organic chemistry, an aldehyde (/ˈældɪhaɪd/) (lat. alcohol dehydrogenatum, dehydrogenated alcohol) is an organic compound containing a functional group with the structure R−CH=O. The functional group itself (without the "R" side chain) can be referred to as an aldehyde but can also be classified as a formyl group. Aldehydes are a common motif in many chemicals important in technology and biology.
Aleksandrów Kujawski railway station
Aleksandrów Kujawski railway station is a railway station serving the town of Aleksandrów Kujawski, in the Kuyavian-Pomeranian Voivodeship, Poland. The station is located on the Kutno–Piła railway and Aleksandrów Kujawski–Ciechocinek railway. The train services are operated by PKP and Przewozy Regionalne.

Polregio
Polregio (formerly Przewozy Regionalne) is a train operator in Poland, responsible for local and interregional passenger transportation. Each day it runs approximately 3,000 regional trains. In 2002 it carried 215 million passengers.

The company was founded in 2001 from the splitup of the PKP Passenger Transport Sector of the once-unitary Polskie Koleje Państwowe national rail operator into several companies to meet European Union requirements.
Van der Linde
Van der Linde is a surname of Dutch origin. Notable people with the surname include:

Angelika van der Linde, German statistician

Christoffel van der Linde (born 1980), South African rugby union player

Etienne van der Linde (born 1978), South African racing driver, uncle of Kelvin

Kelvin van der Linde (born 1996),  South African racing driver, nephew of Etienne

Mary Vanderlinde (1929–2005), American politician

Roald van der Linde (born 1968), Dutch politician

Sheldon van der Linde (born 1999), South African racing driver, younger brother of Kelvin

Wensten van der Linde (born 1990), South African footballer

Dutch van der Linde (born 1850s–1911), character within Red Dead Redemption and Red Dead Redemption 2

Herald Van der Linde, Dutch historian and businessman

Kelvin van der Linde
Kelvin van der Linde (born 20 June 1996) is a South African and German sports car racing driver for BMW Motorsport. He is a two-time champion of the ADAC GT Masters, having won the championship in 2014 and 2019, and won the 24 Hours of Nürburgring in 2017, 2022 and 2025. Van Der Linde formally competed in the Deutsche Tourenwagen Masters for Abt Sportsline. He also made his formula racing debut in Formula E at the 2023 Diriyah ePrix, driving for ABT Cupra as a substitute for the injured Robin Frijns.
2026 Wandsworth London Borough Council election
The 2026 Wandsworth London Borough Council election will take place on 7 May 2026. All 58 members of Wandsworth London Borough Council will be elected. The elections will take place alongside local elections in the other London boroughs and elections to local authorities across the United Kingdom.

Wandsworth London Borough Council
Wandsworth London Borough Council, also known as Wandsworth Council, is the local authority for the London Borough of Wandsworth in Greater London, England. The council has been under Labour majority control since 2022. It is based at Wandsworth Town Hall in the centre of Wandsworth.
Jerzy Hawrylewicz
Jerzy Hawrylewicz (22 December 1958 – 13 February 2009) was a Polish professional footballer who played as a forward. He represented Grunwald Choszczno (1977), Arkonia Szczecin (1977–1978), Stal Stocznia Szczecin (1978–1984), Pogoń Szczecin (1984–1987), and VfB Oldenburg (1987–1992).

On 20 April 1992, during the match against Hannoverscher SC, the then 33-year-old collapsed on the pitch with a heart attack. He suffered from persistent vegetative state syndrome and remained comatose until his death on 13 February 2009.

Arkonia Szczecin
Arkonia Szczecin is a Polish sports club with football and water polo sections based in Szczecin. The water polo team competes in the Ekstraklasa, Poland's top division, and with 13 Polish Championships is one of the most accomplished water polo clubs in Poland. The football team competes in the lower divisions, although it played in the Polish top division in the past.
Timothy Kiptanui
Timothy Kiptanui Too (born 5 January 1980 in Kakiptui) is a Kenyan former 1500 metres runner who finished fourth at the 2004 Summer Olympics. His personal best over 1500 m of 3:30.04 minutes, achieved in 2004, was the third best time in the world that season, only behind Bernard Lagat and Hicham El Guerrouj. He won the Memorial Van Damme meet on the 2004 IAAF Golden League circuit.

He graduated from Nanyuki High School in 1999. In 2003 he won two local meetings and run several races in Europe, although mostly as a pacemaker. The 2004 season proved to be the sole highlight of his career as he did not represent Kenya thereafter or win any major meets. He did not compete in top-level competition after 2009.

He is managed by Gianni Demadonna and coached by Francis Songol.

Kakiptui
Kakiptui (also spelled as Kakiptoi) is a village near Kabiyet in Nandi County, Kenya.

Kakiptui is part of Kipkaren location of Kipkaren division of Nandi County. Its local authority is Nandi County Council and constituency is Mosop.

There is another village named Kakiptui in Kericho County.
Whitehills Hospital
Whitehills Hospital is a health facility in Station Road in Forfar, Angus, Scotland. Formerly an isolation hospital and then a geriatric hospital, in its current form, it is a community hospital known as the Whitehills Health and Community Care Centre. It is managed by NHS Tayside.

Angus, Scotland
Angus (Scots: Angus; Scottish Gaelic: Aonghas) is one of the 32 local government council areas of Scotland, and a lieutenancy area. The council area borders Aberdeenshire, Dundee City and Perth and Kinross. Main industries include agriculture and fishing. Global pharmaceuticals company GSK has a significant presence in Montrose in the east of the county.

Angus was historically a province, and later a sheriffdom and county (called Forfarshire or the County of Forfar until 1928), bordering Kincardineshire to the north-east, Aberdeenshire to the north and Perthshire to the west; southwards it faced Fife across the Firth of Tay. The county included Dundee until 1894, when it was made a county of a city. The pre-1894 boundaries of Angus continue to be used as a registration county. Between 1975 and 1996 Angus was a lower-tier district within the Tayside region. The district took on its modern form and powers in 1996, since when the local authority has been Angus Council.
Costantino Nivola
Costantino (also known as Antine, in Sardinia, or Tino, in the US) Nivola (July 5, 1911 – May 6, 1988) was an Italian sculptor, architectural sculptor, muralist, designer, and teacher.

Born in Orani, a town in the region of Sardinia, Nivola had already started his career when he fled Fascism for Paris in 1938, going to the U.S. in 1939.  His major sculptural work is abstract, large-scale architectural reliefs in concrete, made in his own sandcasting and cement carving processes.  These were erected in and on American buildings between the late 1950s and early 1970s.  Creatively busy and while remaining active in Italy, Nivola also taught at the Harvard Graduate School of Design, Columbia University, UC Berkeley, and elsewhere.

The Nivola Museum in Orani, Sardinia is dedicated to his life and sculpture, and hosts the largest collection of his smaller scale work.

McCormick Place
McCormick Place is a convention center in Chicago. It is the largest convention center in North America. It consists of four interconnected buildings and one indoor arena sited on and near the shore of Lake Michigan, about 1.0 mi (1.6 km) south of the Chicago Loop. McCormick Place hosts numerous trade shows and meetings.  The largest regular events are the Chicago Auto Show each February, the International Home and Housewares Show each March, the National Restaurant Association Annual Show each May, and the International Manufacturing Technology Show in the fall every other year.
Ubrogepant
Ubrogepant, sold under the brand name Ubrelvy, is a medication used for the acute (immediate) treatment of migraine with or without aura (a sensory phenomenon or visual disturbance) in adults. It is not indicated for the preventive treatment of migraine. Ubrogepant is a small-molecule calcitonin gene-related peptide receptor antagonist. It is the first drug in this class approved for the acute treatment of migraine.

The most common side effects are nausea, tiredness and dry mouth. Ubrogepant is contraindicated for co-administration with strong CYP3A4 inhibitors.

Fatigue
Fatigue is a state of being without energy for a prolonged period of time. Fatigue is used in two contexts: in the medical sense, and in the sense of normal tiredness.

In the medical sense, fatigue is seen as a symptom, and is sometimes associated with medical conditions including autoimmune disease, organ failure, mood disorders, heart disease, infectious diseases, and post-infectious-disease states. However, fatigue is complex and in up to a third of primary care cases no medical or psychiatric diagnosis is found.

In the sense of tiredness, fatigue often follows prolonged physical or mental activity. Physical fatigue results from muscle fatigue brought about by intense physical activity. Mental fatigue results from prolonged periods of cognitive activity which impairs cognitive ability, can manifest as sleepiness, lethargy, or directed attention fatigue, and can also impair physical performance.
Jimmy Reynolds
James Russel Reynolds (August 5, 1904 – February 16, 1963) was an American jazz pianist.

Reynolds led his own band at the Hollywood Cafe in New York City in the 1930s and 1940s, though he rarely recorded with this ensemble. He also played as a sideman with Kaiser Marshall (1935) and recorded with Red Allen, Jabbo Smith (1938), Hot Lips Page (1938–40, on sides for Decca Records), Bill Dillard (1947), and Larry Darnell (1952). He played with Harry Dial and Lester Boone in the 1960s.

Larry Darnell
Larry Darnell (born Leo Edward Donald, Jr.; December 17, 1928, Columbus, Ohio – July 3, 1983, Columbus) was a successful American singer, who was instrumental in the formation of the New Orleans style of R&B in the late 1940s and early 1950s.
Parchment paper
Parchment paper, also known as baking paper, is a cellulose-based paper whose material has been processed so as to obtain additional properties such as non-stickiness, grease resistance, resistance to humidity and heat resistance. It is commonly used in baking and cooking as a disposable non-stick paper. It is greaseproof paper that can be used for several different applications, its surface prevents the food from sticking, and also is highly heat-resistant with some brands capable of temperatures up to 420 °F (216 °C). It should not be confused with waxed paper, which is paper that has been coated with wax.

Non-stick surface
A non-stick surface is engineered to reduce the ability of other materials to stick to it. Non-sticking cookware is a common application, where the non-stick coating allows food to brown without sticking to the pan. Non-stick is often used to refer to surfaces coated with polytetrafluoroethylene (PTFE), a well-known brand of which is Teflon. In the twenty-first century, other coatings have been marketed as non-stick, such as anodized aluminium, silica, enameled cast iron, and seasoned cookware.
Chládek
Chládek (feminine: Chládková, in Slovak also Chládeková) is a Czech and Slovak surname. It is derived from the word chlad, meaning 'coolness.' Notable people with the surname include:

Anton Chladek (1794–1882), Romanian painter

Dana Chladek (born Dana Chládková; 1963), Czech-American kayaker

Denisa Chládková (born 1979), Czech tennis player

Marcel Chládek (born 1968), Czech politician

Patrícia Chládeková (born 1997), Slovak footballer

Zdeněk Chládek (born 1990), Czech boxer

Marcel Chládek
Marcel Chládek (born 9 April 1968) is a Czech social-democratic politician and former senator for Louny (2008 until 2014). He served as Minister of Education, Youth and Sports of the Czech Republic from 29 January 2014 until 6 June 2015.
Steeler Nation
Steeler Nation is an official name for the fan base of the National Football League's Pittsburgh Steelers. The term was coined by NFL Films narrator John Facenda in the team's 1978 highlights film. Steelers Country is often used for the Pittsburgh, Pennsylvania, area where the fan base originates or for areas with a large Steelers fan base.

Franco Harris
Franco Harris (March 7, 1950 – December 20, 2022) was an American professional football player who was a fullback for 13 seasons in the National Football League (NFL), primarily with the Pittsburgh Steelers. He played college football for the Penn State Nittany Lions and was selected by the Steelers in the first round of the 1972 NFL draft. Harris spent his first 12 seasons with Pittsburgh, earning nine Pro Bowl selections, and was a member of the Seattle Seahawks in his last.

A four-time Super Bowl winner with the Steelers, Harris was the Most Valuable Player (MVP) of Super Bowl IX. He also scored the "Immaculate Reception" touchdown, one of professional football's most famous plays, which gave the Steelers their first-ever playoff win. Harris was inducted into the Pro Football Hall of Fame in 1990.
9 Nelalu
9 Nelalu or Tommidi Nelalu (transl. 9 Months) is a 2000 Telugu-language drama film directed by Kranthi Kumar. It starred Soundarya and Vikram. It opened to positive reviews from critics and was later re-shot and released in Tamil as Kanden Seethaiyai (transl. I saw Seetha), due to Vikram's newfound popularity post-Sethu. The film was premiered retrospective at the Toronto International Film Festival; Kumar shot the film in  a record 15 days. Noted directors V. V. Vinayak and Surender Reddy worked as assistant directors on the film. The film was a box office flop although Soundarya's performance was praised.

Sethu (film)
Sethu (/seɪθu/) is a 1999 Indian Tamil-language romantic drama tragedy film, written and directed by Bala in his debut. The film stars Vikram and Abitha. The score and soundtrack were composed by Ilaiyaraaja, with cinematography by R. Rathnavelu and editing by Raghu Baabu.

Sethu, released on 10 December 1999, initially began running as a single noon show in a suburban theatre, but gradually built up audiences through word-of-mouth publicity. The film became a sleeper hit and Vikram's first major breakthrough film. It won the National Film Award for Best Tamil Feature Film and the Best Film award at the Filmfare Awards and the Cinema Express Awards. Bala and Vikram also won several awards for their contributions. The film was remade in Kannada as Huchcha, in Telugu as Seshu and in Hindi as Tere Naam.
Ricardo Rodríguez-Pace
Ricardo Rodríguez-Pace (born 28 April 1993) is a Venezuelan professional tennis player. He achieved a career high ATP ranking of World No. 282 on 9 June 2014. He reached his highest doubles ranking in October 2016 of No. 670. 
He has won eleven ITF titles in singles and nine in doubles. He is currently the No. 2 Venezuelan player.

Rodríguez is also a member of the Venezuela Davis Cup team where he holds the record of most singles victories in the history of Venezuela (22-9) in 17 appearances.

ATP rankings
The PIF ATP Rankings (previously known as the Pepperstone ATP Rankings) are the merit-based method used by the Association of Tennis Professionals (ATP) for determining the qualification for entry as well as the seeding of players in all singles and doubles tournaments. The first rankings for singles were published on 23 August 1973 while the doubles players were ranked for the first time on 1 March 1976. Ranking points are awarded according to the stage of tournament reached, and the prestige of the tournament, with the four Grand Slam tournaments awarding the most points. The rankings are updated every Monday, and points are dropped 52 weeks after being awarded (with the exception of the ATP Finals, from which points are dropped on the Monday following the last ATP Tour event of the following year). As of February 27,
2026, Carlos Alcaraz is the current men's singles world No. 1.