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

Invariant subspace
In mathematics, an invariant subspace of a linear mapping T : V → V  i.e. from some vector space V to itself, is a subspace W of V that is preserved by T.  More generally, an invariant subspace for a collection of linear mappings is a subspace preserved by each mapping individually.
Jeong Yun-hui
Jeong Yun-hui (Korean: 정윤희; born June 4, 1954) is a former South Korean actress active since 1975. She was born in Tongyeong, a southwestern coastal city of South Gyeongsang Province, South Korea in 1954. After graduation from Hyehwa Girls' High School, Jeong debuted as an actress in 1975 as starring in Yokmang directed by Lee Gyeong-tae. Jeong was commonly referred to as one of the "New Troika" or "Second Troika" along with her rival actresses, Chang Mi-hee and Yu Ji-in of the 1970s and 1980s after the "First Troika", Moon Hee, Nam Jeong-im, and Yoon Jeong-hee of the 1960s.

Nam Jeong-im
Nam Jeong-im (Korean: 남정임; July 21, 1945 – September 2, 1992)  was a South Korean actress. Nam was commonly referred to as one of the "Troika" along with her rival actresses, Yoon Jeong-hee and Moon Hee of the 1960s and early 1970s.
Rio Rancho City Council
The Rio Rancho City Council is the elected legislative authority of the city of Rio Rancho, New Mexico. It consists of 6 members, elected from respective districts of the city on a non-partisan basis. The form of city government is council–manager government and home rule municipality. It meets in the New Council chambers at the Rio Rancho city hall in the northwest quadrant of the city.

Rio Rancho, New Mexico
Rio Rancho (Spanish: Río Rancho) is the largest and most populous city in Sandoval County, New Mexico, United States. A small portion of the city extends into northern Bernalillo County. Part of the expansive Albuquerque metropolitan area, it is the third-largest city in New Mexico, and one of the most rapidly growing. Rio Rancho had a population of 104,046 at the 2020 census. The name Rio Rancho derives from Los Ranchos, the Spanish colonial ranches established along the Rio Grande in the Albuquerque Basin, and throughout historic Nuevo México. There were large ranches also in neighboring Corrales. Since the late 20th century, it has developed as a suburb of Albuquerque.
Astellas Cycling Team
Astellas Cycling Team was an American UCI Continental cycling team. The team was originally established in 2012 as a Domestic Elite team under the name Astellas Oncology Cycling Team. The team turned professional and stepped up to UCI Continental status in 2014. In September 2016 the team confirmed that it had disbanded due to sponsor Astellas Pharma choosing to discontinue its funding, with the team having competed in its final race, the Boston Mayor's Cup, earlier that month.

Astellas Pharma
Astellas Pharma Inc. (アステラス製薬株式会社, Asuterasu Seiyaku Kabushiki-gaisha) is a Japanese multinational pharmaceutical company, formed on 1 April 2005 from the merger of Yamanouchi Pharmaceutical Co., Ltd. (山之内製薬株式会社, Yamanouchi Seiyaku Kabushiki-gaisha) and Fujisawa Pharmaceutical Co., Ltd. (藤沢薬品工業株式会社, Fujisawa Yakuhin Kōgyō Kabushiki-gaisha).

Astellas is a member of the Mitsubishi UFJ Financial Group (MUFJ) keiretsu.
Spiculogloeomycetes
The Spiculogloeomycetes are a class of fungi in the subdivision Pucciniomycotina of the Basidiomycota. The class consists of a single order, the Spiculogloeales, together with an additional, unassigned genus, Meniscomyces. Many species are currently known only from their yeast states. Species in the genus Spiculogloea form hyphal states that produce auricularioid (laterally septate) basidia and are parasitic on other fungi.

Pucciniomycotina
Pucciniomycotina is a subdivision of fungus within the division Basidiomycota. The group was known as Urediniomycetes until 2006, when it was elevated from a class to a subdivision and named after the largest order in the group, Pucciniales.

The subdivision contains 10 classes, 21 orders, and 38 families. Over 8400 species of Pucciniomycotina have been described; thus, the subdivision contains more than 8% of all described fungi.

Pucciniomycotina appears to be sister to Agaricomycotina, based on maximum-likelihood analysis of six genes.
Knightsville, Utah
Knightsville (also known as Knightville) is a ghost town located in the East Tintic Mountains on the northern slope of Godiva Mountain, approximately 2 miles (3.2 km) east of Eureka, in the northeastern corner of Juab County in central Utah, United States. A silver mining camp, Knightsville was established and operated as a company town by local mining entrepreneur Jesse Knight. The town was inhabited from 1896 until approximately 1940.

Eureka, Utah
Eureka is a city in Juab County, Utah, United States. It is part of the Provo–Orem metropolitan area. The population was 662 at the 2020 census, down from 669 in 2010.

The city was named from the Greek word eureka, meaning "I have found it!"
Degrassi: Next Class season 1
The first season of Degrassi: Next Class (previously known as Degrassi) premiered on January 4, 2016, in Canada and was released on January 15, 2016, internationally. It was the first season to air on Family in Canada and on Netflix internationally.

This season follows a group of high school sophomores and juniors from Degrassi Community School, a fictional school in Toronto, Ontario, and depicts some of the typical issues and challenges common to a teenager's life. This season will depict a new school year after the previous seniors, some of whom debuted during "The Next Generation", graduated in the previous season. This season will feature another rebranding for the series and is being considered a stand-alone series.

Degrassi: Next Class
Degrassi: Next Class is a Canadian teen drama television series primarily created by Linda Schuyler. The fifth and to date most recent series in the Degrassi franchise and a direct sequel to Degrassi: The Next Generation, it premiered on Family Channel's new teen programming block F2N in Canada on January 4, 2016, and was released on Netflix internationally on January 25, 2016.

The series follows most of the same characters that had debuted in the final four seasons of the previous series, as well as introducing new characters. Intended as the fifteenth season of Degrassi: The Next Generation, it was later retooled to be a reboot that would appeal to the emerging Generation Z. Like its predecessor, the series was filmed at the Epitome Pictures studios in Toronto, Ontario.

The fourth season, released to Netflix in July 2017, was the last; in March 2019, show producer and frequent director Stefan Brogren alluded to the show's cancellation in a tweet.
Ohio's 6th congressional district
Ohio's 6th congressional district is a U.S. congressional district which is represented by Representative Michael Rulli of the Republican Party. Rulli was elected to the seat after he defeated Democrat Michael Kripchak in the June 11, 2024 special election, caused by the resignation of incumbent Bill Johnson (R) on January 21, 2024.

This district runs along the eastern side of the state, bordering West Virginia and Pennsylvania. It stretches from Marietta through several Ohio River industrial towns all the way to the city of Youngstown.

Vinton County, Ohio
Vinton County is a county located in the U.S. state of Ohio. As of the 2020 census, the population was 12,800, making it the least populous county of Ohio. Its county seat is McArthur. The county is named for Samuel Finley Vinton, a US Representative from Ohio (1823–37, 1843–51).
Quamichan Lake
Quamichan Lake is a lake in the Cowichan Valley region of Vancouver Island, British Columbia, Canada, located three kilometres to the northeast of the City of Duncan.

Quamichan Lake and its sister Somenos Lake were created 11,000 years ago by receding glaciers. Both lakes contribute to Cowichan River. Quamichan Lake's outflow is Quamichan Creek which joins with Somenos Creek, the outflow from Somenos Lake, which flows to Cowichan River.

The Cowichan Watershed Board identifies a common set of conditions for both shallow lakes:

excessive nutrient loading from the farms and homes which surround the lakes

insufficient "flushing" in summer due to reduced inflows and truncated outflows

increased plant growth ("algae-blooms"), and

eutrophication (reduced oxygen as the vegetation decomposes)

intensified warming

In autumn 2016, the lake's algae received public attention after news coverage of its killing at least four dogs.

Cowichan Valley
The Cowichan Valley is a region around the Cowichan River, Cowichan Bay and Cowichan Lake on Vancouver Island, in British Columbia, Canada. There is some debate as to the origin of the name Cowichan, which many  believe to be an anglicized form of the First Nations tribal name Quw'utsun.
Czech Republic men's national volleyball team
The Czech Republic national men's volleyball team is controlled by the Czech Volleyball Federation, which represents the country in international competitions and friendly matches. Czech Republic is ranked 22nd (as of January 2023) in the FIVB world ranking.

FIVB considers Czech Republic as the inheritor of the records of Czechoslovakia (1948–1993). The Czech team’s first participations in international competitions saw them win a gold medal at the inaugural European Championship in 1948 which kick-started a golden age for the team. They won two more European in 1955 and 1958, two golds at the World Championships of 1956 and 1966, and a further eight medals in other elite tournaments. They took silver at the Tokyo 1964 Olympic Games and followed that with the bronze four years later in Mexico City.

2021 Men's European Volleyball Championship
The 2021 Men's European Volleyball Championship was the 32nd edition of the Men's European Volleyball Championship, organised by Europe's governing volleyball body, CEV. For the second time, the EuroVolley was held in four countries: Poland, Czech Republic, Estonia and Finland. The number of national teams that participated in the event remained to 24.

In Poland, matches were played in Gdańsk, Katowice and Kraków.
In Finland, matches were played in Tampere.
In Czech Republic, matches were played in Ostrava.
In Estonia, matches were played in Tallinn. The top two teams of the tournament qualified for the 2022 FIVB Volleyball Men's World Championship as the CEV representatives.

Italy won their 7th title of Men's European Volleyball Championship. Simone Giannelli was chosen as MVP of this tournament.
Kotyrkol
Kotyrkol (Kazakh: Қотыркөл) is a salt lake in Birzhan sal District, Akmola Region, Kazakhstan.

Stepnyak town, the district capital, is located 5 kilometers (3.1 mi) to the NNE of the northern lakeshore.

Birzhan sal District
Birzhan sal District (Kazakh: Біржан сал ауданы) is a district of Akmola Region in northern Kazakhstan. The administrative center of the district is the town of Stepnyak. In 2017, Enbekshilder District was renamed Birzhan sal District. Population: 17,930 (2009 census results); 25,599 (1999 census results).
Arpan Thapa
Arpan Thapa (Nepali: अर्पण थापा) (born 15 November 1978) is a Nepalese actor, director, and scriptwriter.

He studied acting in Mumbai in 2002 before returning to Nepal to start his career in the Nepali film industry. He sold CDs at Mahabouddha, to promote the business of a friend, where he met Murray Kerr, the director.

Thapa began his acting career with the Nepali film Sick City, playing the lead role as Krishna. He has directed the movie Mukhauta, which was released on 13 June 2014.

Thapa cites Daniel Day-Lewis as his inspiration and has expressed respect for other Nepalese actors, including Hari Bansha Acharya and Madan Krishna Shrestha.

Madan Krishna Shrestha
Madan Krishna Shrestha  (Nepali: मदन कृष्ण श्रेष्ठ; listenⓘ) is a Nepali actor, comedian, writer, singer, song writer, composer, director and producer.  He is one of the most successful and respected comedians in the Nepali entertainment industry and was the most popular stage performer of his time.

He is well known for his method acting. He is one of the comedy duo from MaHa Jodi, the other one being Hari Bansha Acharya. He also performs on stage most of the time with his partner, Hari Bansha Acharya.
Portland and Western Railroad
The Portland and Western Railroad (reporting mark PNWR) is a 478-mile (769 km) Class II railroad serving the U.S. state of Oregon, and is a wholly owned subsidiary of shortline and regional railroad holding company Genesee & Wyoming Inc. The PNWR includes a subsidiary, the Willamette and Pacific Railroad (reporting mark WPRR).

PNWR's tracks lie entirely within Oregon, extending from Astoria to Portland along the Columbia River, from Portland to Eugene through the Willamette Valley, and along several spurs through the Northern Oregon Coast Range.

Tigard, Oregon
Tigard (/ˈtaɪɡərd/ ⓘ TY-gərd) is a city in Washington County, Oregon, United States. The population was 54,539 at the 2020 census, making it the 12th most populous city in Oregon. Incorporated in 1961, the city is located south of Beaverton and north of Tualatin, and is part of the Portland metropolitan area. Interstate 5 and Oregon Route 217 are the main freeways in the city, with Oregon Route 99W and Oregon Route 210 serving as other major highways. Public transit service is provided by TriMet, via several bus routes and the WES Commuter Rail line.
Wallaceville railway station
Wallaceville railway station is a suburban railway station serving Wallaceville in Upper Hutt, New Zealand. The station is located on the Hutt Valley section of the Wairarapa Line, 31.3 km (19.4 mi) north of Wellington, and is served by Metlink on behalf of the Greater Wellington Regional Council. Trains between Upper Hutt and Wellington stop at Wallaceville.

There is a large park and ride facility as well as bicycle lockers.

The Blue Mountains Campus  at Wallaceville is to be the location for KiwiRail's national Train Control Centre, which is to move from the Wellington railway station; to house a team of 120 train control team members in a 2700 square metres train control room. It iwill be next to the rail network.

Public transport in the Wellington Region
Public transport in the Wellington Region, branded under the name Metlink, is the public transport system serving Wellington and its surrounding region. It is the most used public transport system in New Zealand per capita, and consists of electric and diesel buses, suburban trains, ferries and a funicular  (the Wellington Cable Car). It also included trams until 1964, and trolleybuses until 2017.

Buses and ferries are privately owned, with the infrastructure owned by public bodies, and public transport is often subsidised. The Greater Wellington Regional Council is responsible for planning and subsidising public transport, and pays around $30 million for bus and train services each year. The system covers Wellington City, Lower Hutt, Upper Hutt, Porirua, the Kāpiti Coast and the Wairarapa.
M. Kothandapani
M. Kothandapani was an Indian politician and former Member of the Legislative Assembly of Tamil Nadu. He was elected to the Tamil Nadu legislative assembly as an All India Anna Dravida Munnetra Kazhagam candidate from Tirupporur constituency in the 2016.

He was one of the 18 members who were disqualified were disqualified by Speaker P. Dhanapal as they withdrew support to Chief Minister Edappadi K. Palaniswami and became loyal to rebel leader T.T.V. Dhinakaran and joined his party Amma Makkal Munnetra Kazhagam.

P. Dhanapal
P. Dhanapal (born 16 May 1951) is an Indian politician and incumbent Member of the Legislative Assembly of Tamil Nadu. He is a former Speaker of Tamil Nadu Legislative Assembly.

P. Dhanapal  was born on 16 May 1951 in Karupur. He obtained a master's degree and is married with two children.

Dhanapal was elected to the Tamil Nadu Legislative Assembly as an All India Anna Dravida Munnetra Kazhagam candidate from Sankagiri constituency in the 1977, 1980 and 1984 and 2001 elections. In the 2011 and 2016 Tamil Nadu assembly elections he won from Rasipuram and Avanashi constituencies, respectively.
Loxford Park Speedway
The Loxford Park Speedway is a motorcycle speedway track located in the area of Loxford, near Kurri Kurri in New South Wales, Australia. It is home to the Kurri Kurri Speedway Club and the Kurri Cobras. Loxford Park also has a 135 m (148 yd) junior track, built on the infield of the main track with the junior track joining onto the main straight and sharing the start-finish line. The site also hosts sidecar racing.

2023 Australian Individual Speedway Championship
The 2023 Australian Individual Speedway Championship was a motorcycle speedway competition organised by Motorcycling Australia (MA) for the Australian Individual Speedway Championship. The event was held over four rounds.

Jack Holder won his first Australian title.
Château Phélan Ségur
45°15′42″N 0°46′06″W﻿ / ﻿45.26161°N 0.76846°W﻿ / 45.26161; -0.76846

Château Phélan Ségur lies in the commune of Saint-Estèphe in the Bordeaux region of France, neighbouring vineyards Château Calon-Ségur and Château Montrose. In a 2003 Cru Bourgeois classification revision, it was listed as one of 9 Cru Bourgeois Exceptionnels.

A second wine is produced since 1986, under the label Frank Phelan. A more recent venture is a wine titled La Croix Bonis.

Château Montrose
45°14′48″N 0°45′40″W﻿ / ﻿45.24667°N 0.76114°W﻿ / 45.24667; -0.76114

Château Montrose is a winery in the Saint-Estèphe appellation of the Bordeaux region of France. The wine produced here was classified as one of fifteen Deuxièmes Crus (Second Growths) in the original Bordeaux Wine Official Classification of 1855. Since 2006, Olivier and Martin Bouygues own this winery.
Mayor of Otaki
The Mayor of Otaki officiated over the Otaki Borough of New Zealand, which was administered by the Otaki Borough Council. The office existed from 1921 until 1989, when Otaki Borough and was amalgamated into the new Kāpiti Coast District Council as part of the 1989 local government reforms. There were 10 holders of the office.

Ōtaki, New Zealand
Ōtaki is a town in the Kāpiti Coast District of the North Island of New Zealand, situated halfway between the capital city Wellington, 70 km (43 mi) to the southwest, and Palmerston North, 70 km (43 mi) to the northeast.

Ōtaki is located on New Zealand State Highway 1 and the North Island Main Trunk railway between Wellington and Auckland and marks the northernmost point of the Wellington Region.

The New Zealand Ministry for Culture and Heritage gives a translation of "place of sticking a staff into the ground" for Ōtaki.
Kosong County
Kosŏng ([ˈkɤsɔŋ‿ɡun]) is a kun, or county, in Kangwŏn province, North Korea.  It lies in the southeasternmost corner of North Korea, immediately north of the Korean Demilitarized Zone.  Prior to the end of the Korean War in 1953, it made up a single county, together with what is now the South Korean county of the same name.  In a subsequent reorganization, the county absorbed the southern portion of Tongch'ŏn county.

Mount Kumgang Tourist Region
The Mount Kumgang Tourist Region was a special administrative region of North Korea. It was established in 2002 to handle South Korean tourist traffic to Mount Kumgang (Diamond Mountain). It was one of the symbols of the South Korean Sunshine Policy. In January 2024, North Korea announced that they would close the Mount Kumgang International Tourism Administration.
LDC Radio
LDC Radio is a community radio station based in the city of Leeds, West Yorkshire, with a dance and urban music format. Its studios are based in Leeds city centre. Its name is an abbreviation of Leeds Dance Community Radio.

Community radio in the United Kingdom
In the United Kingdom, community radio refers to a system of licensing small, micro-local, non-profit radio stations, which started in 2002. In its early days, the pilot scheme was known as access radio. New legislation paved the way for this additional tier of radio, starting in 2005, and hundreds of community stations have since been set up. Unlike commercial radio licensing, which is generally advertised to cover a specific region, community radio stations are usually limited to broadcast areas smaller than commercial or BBC local stations, nominally within a 5 kilometres (3.1 mi) radius of their transmitter.
Hadji Ali Haseki
Hadji Ali Haseki (Turkish: Hacı Ali Haseki, Greek: Χατζή Αλής Χασεκής) was an 18th-century Ottoman Turk and for twenty years (1775–1795) on-and-off ruler of Athens, where he is remembered for his cruel and tyrannical rule.

Franz Babinger
Franz Babinger (15 January 1891 – 23 June 1967) was a German orientalist and historian of the Ottoman Empire, best known for his biography of the Ottoman sultan Mehmed II, known as "the Conqueror", originally published as Mehmed der Eroberer und seine Zeit. An English translation by Ralph Manheim is available from the Princeton University Press, under the title Mehmed the Conqueror and His Time.
1966 PGA Tour Qualifying School graduates
This is a list of the 1966 PGA Tour Qualifying School graduates. The tournament was played over 144 holes at the PGA National Golf Club in Palm Beach Gardens, Florida in late October. The tournament represented the totality of the year's PGA Tour Qualifying School; there were no local or regional sections.

PGA Tour Qualifying Tournament
The annual PGA Tour Qualifying Tournament, also known as Qualifying School or Q-School, was historically the main method by which golfers earned PGA Tour playing privileges, commonly known as a Tour card. From 2013 to 2022, Q-School granted privileges only for the Korn Ferry Tour, the PGA Tour's official developmental circuit, but in 2023 it began to again award a small number of PGA Tour cards.
Zeta Volantis
Zeta Volantis, Latinized from ζ Volantis, is a binary star system in the southern constellation of Volans. It has an apparent visual magnitude of 3.92, which is bright enough to be seen with the naked eye. Based upon parallax measurements by the Gaia spacecraft, it is approximately 145 light-years (44.6 parsecs) from the Sun. The companion is a magnitude 9.7 star at an angular separation of 16.7″. Based upon their motion through space, this system made its perihelion passage some 858,000 years ago when it came within 22 ly (6.6 pc) of the Sun. It is currently moving away with a radial velocity of 48 km/s.

The primary component is K-type giant star with a stellar classification of K0 III. It has a derived luminosity of around 60 times that of the Sun, 1.2 times the Sun's mass and is about 5.1 billion years old. At this age, it has expanded to 10.7 times the Sun's size. The expanded outer envelope has an effective temperature of 4,788 K, giving it the orange glow of a K-type star.

Volans
Volans is a constellation in the southern sky. It represents a flying fish; its name is a shortened form of its original name, Piscis Volans. Volans was one of twelve constellations created by Petrus Plancius from the observations of Pieter Dirkszoon Keyser and Frederick de Houtman and it first appeared on a 35-cm (14") diameter celestial globe published in 1597 (or 1598) in Amsterdam by Plancius with Jodocus Hondius. The first depiction of this constellation in a celestial atlas was in Johann Bayer's Uranometria of 1603.