OpenLLM-France/wikimedia huggingface dataset:
# André Soares (fighter)

André "Gigueto" Soares is a Brazilian jiu-jitsu and mixed martial arts fighter. He competes in the flyweight division, and is also an instructor.

## History

Shares started training in martial arts at 9 years old practicing Judo. At the age of 15 he fell in love with Brazilian jiu-jitsu. When he was a purple belt he was invited to try out for the Carlson Gracie Competition Team. To make the team there was a tournament style training session in the middle of Carlson Gracie's gym. He won the tournament and became a Team A competitor. His skills grew quickly and he won the Brazilian Nationals in 1998. He trained with Carlson Gracie for five years until Carlson moved to the US and the team split up. Soares followed his teammates over to BTT (Brazilian Top Team) where he competed and received his black belt in 2001. He came in second in the 2002 World Championships.
In 2004, he moved to Florida to reunite with ATT (American Top Team) founder Ricardo Liborio and his master Marcus Aurelio. Soares competed in MMA and jiu-jitsu in America. He won Hawaii Shooto 2005, and took first in the Arnold Schwarzenegger/Gracie World Submission championships.

## Mixed martial arts record

Professional record breakdown :
| 7 matches | 5 wins | 2 losses |
| By knockout | 0 | 0 |
| By submission | 4 | 0 |
| By decision | 1 | 2 |
| Res. | Record | Opponent | Method | Event | Date | Round | Time | Location |
| Loss | 5-2 | Zach Makovsky | Decision (unanimous) | EliteXC: Primetime | May 31, 2008 | 3 | | New Jersey, United States |
| Win | 5-1 | Josh Spearman | Submission (guillotine choke) | BCX 4 - Battle Cage Xtreme 4 | April 19, 2008 | 1 | 0:19 | New Jersey, United States |
| Win | 4-1 | Matt McCabe | Submission (armbar) | CITC 3 - Marked Territory | September 30, 2006 | 1 | 1:09 | Collins Arena, Brookdale College, Lincroft, NJ. |
| Win | 3-1 | Ryan Lee | Submission (triangle choke) | Shooto Hawaii - Unleashed | March 25, 2005 | 1 | 2:38 | Hawaii, United States |
| Win | 2-1 | Jim Bruketta | Submission (armbar) | FCC 18 - Freestyle Combat Challenge 18 | March 5, 2005 | 1 | | Wisconsin, United States |
| Loss | 1-1 | Tom Niinimaki | Decision | CWFC 9 - Xtreme Xmas | December 18, 2004 | 3 | 5:00 | England |
| Win | 1-0 | Ulises Rocha | Decision (unanimous) | IC 8 - Ethereal | November 20, 2004 | 2 | 5:00 | Indiana, United States |
# Ryan Gentles (actor)

Ryan Gentles is an American actor who has worked with Tyler Perry studios in several stage plays and movies including Madea Goes to Jail playing Nate, Sonny's boss and Vanessa's boyfriend. He also made an appearance in the movie version of "Madea's Family Reunion" as a stripper. He appeared In the stage play What's Done in the Dark and was Jennifer Hudson's love interest in her hit video "Spotlight". Gentles made his theatrical debut in E. Lynn Harris' play Not a Day Goes By in which he played Zurich, a sports agent. Gentles has also appears in stage plays by John Ruffin and TJ Hemphill and is a regular celebrity trainer and personality on the annual Tom Joyner Fantastic Voyage.
# Achilles bursitis

Achilles bursitis is bursitis (inflammation of synovial sac) of bursa situated above the insertion of tendon to calcaneus. It results from overuse and wearing of tight shoes.
# Brian Price

Brian Price may refer to:
* Brian Price (rowing) (born 1976), Canadian coxswain
* Brian Price (rugby union) (1937–2023), Welsh rugby union international
* Brian Price (American football, born 1989), American football defensive tackle
* Brian Price (American football, born 1994), American football defensive tackle
* Brian David Price, American screenwriter and screenwriting teacher
* Brian R. Price, American author, editor, armorer, and publisher
* Bryan Price (born 1962), American former baseball manager of the Cincinnati Reds
* Bryan Price (pitcher) (born 1986), American baseball player
# Caterham Common

Caterham Common near Caterham in Surrey was the venue for three historic cricket matches played from 1767 to 1769. In the 18th century, it was the home venue of the Caterham Cricket Club, run by Henry Rowett.
# Sanders House (Little Rock, Arkansas)

The Sanders House is a historic house at 2100 Gaines Street in Little Rock, Arkansas. It is a two-story brick structure, topped by a gabled tile roof. Its facade is three bays wide, with a center entrance sheltered by a rounded porch supported by Tuscan columns. Windows in the side bays are sash, while that above the entrance is a band of four casement windows with Prairie School style. The house was built in 1917 to a design by local architect Theo Sanders.
The house was listed on the National Register of Historic Places in 1982.
# Beyer, Pennsylvania

Beyer is an unincorporated community in Indiana County, Pennsylvania, United States. The community is located on Pennsylvania Route 85 1 mile (1.6 km) west-southwest of Plumville. Beyer has a post office with ZIP code 16211, which opened on May 13, 1918.
# Acleisanthes crassifolia

Acleisanthes crassifolia, the Texas trumpets, is a plant in the family Nyctaginaceae. It is found in North America and Mexico and is native to southwestern counties of Texas and northeastern Mexico. These plants grow low to the ground with the stem of these fully grown plants between 15 cm to 20 cm long. There are few other species of Acleisanthes that inhabit the same areas. However, Texas trumpets can be easily identified throughout the year based on their thick and dark green leaves which has white veins. Acleisanthes crassifolia is a perennial herbaceous plant with fruits and flowers.

## Distribution

Acleisanthes crassifolia naturally occurs in Southwestern Texas counties and in Mexico. They can be found in Maverick, Val Verde, and Kinney counties, and in Coahuila, Mexico.

## Habitat and ecology

Acleisanthes crassifolia is a perennial plant that grows in well-drained, gravelly loams of areas with changing elevations/slopes, usually found in scattered vegetated regions of shrub lands. This plant is adapted to semiarid weather conditions. Its environmental precipitation range is from 330mm to 610mm/yr, and temperature range from 10 to 43 degree Celsius.

## Morphology

Individuals of this species are subshrubs that have horizontal shoots low to the ground. These plants grow low to the ground with 15–50 cm long prostrate and procumbent stems. It has opposite leaves in pairs which are not equal in size. The blades are 1/3 to 2/3 bigger than the petioles. The plant's petioles are thick and ovate shaped with rough surface, 5–45 mm long and 2–30 mm wide, sharp to dull but particularly sharp at the apex and triangular to round shaped at the base. Leaves are elliptical shaped, thick and dark green with white pinnate and undulate white veins. Flowers are axillary, separate from each other (not on the same stem), and attached directly to the base of stem.

## Flowers and fruit

Flowers of Acleisanthes crassifolia are chasmogamous or cleistogamous. Petals of corolla in Cleistogamous flowers are green and 2–6 mm long. The petals of corolla of chasmogamous flowers are white, projected outward and shaped like a funnel, 5-lobed petals that are 8-25mm wide. The fruits are 5-angled, elongated and oval shaped, 6–9 mm long and 3–4 mm wide, minutely narrow at both ends, has light longitudinally concaved lines along with 5 wide low ribs without resinous glands, fruit body surface has small white hairs that are pressed towards the body.
# 31st Battalion

31st Battalion may refer to:
* 31st Battalion, Royal Queensland Regiment, a unit of the Australian Army
* 31st/42nd Battalion, Royal Queensland Regiment, a unit of the Australian Army
* 2/31st Battalion (Australia), a unit of the Australian Army that was raised during World War II
* 31st (Alberta) Battalion, CEF, a unit of the Canadian Army
* 31st Infantry Battalion (Estonia), a unit of the Estonian Army
* 31st Engineer Battalion, a unit of the United States Army
* Combat Logistics Battalion 31, a unit of the United States Marine Corps
# Darninae

Darninae is a subfamily of treehoppers belonging to the family Membracidae. It includes 5 tribes and about 30 genera.

## Tribes and genera

* Cymbomorphini
** Cymbomorpha
** Eumela
** Fermeria
** Germariana
* Darnini
** Alcmeone
** Allocyphotes
** Alobia
** Andinodarnis
** Cyphotes
** Darnis
** Dectonura
** Hebetica
** Hebeticoides
** Hypheodana
** Leptosticta
** Nasuconia
** Ochrolomia
** Peltosticta
** Stictopelta
** Sundarion
** Taunaya
* Hemikypthini
** Atypa
** Hemikyptha
** Neoproterpia
* Hyphinoini
** Bubalopa
** Eualthe
** Hanstruempelia
** Hyphinoe
** Tomogonia
* Procyrtini
** Procyrta
# Somma Lombardo

Somma Lombardo (Suma in lombard) is a town in the province of Varese, Lombardy, Italy. It received the honorary title of city with a presidential decree on 16 June 1959.

## Industry

The airline Neos has its head office in the city.

## History

The town was strategically located on the consular Roman road, passing from the town of Sesto Calende and linking Milan to Verbano.
In medieval times, the city was under the jurisdiction of the nearby town of Arsago Seprio, an important political centre of the region.
In the forest around Somma, various vestiges of trenches and landing strips dating back to the Second World War can still be found.

## People

* Giuseppina Aliverti (1894–1982), geophysicist remembered for developing the Aliverti-Lovera method of measuring the radioactivity of water
* Niccolò Sfondrati, Pope Gregory XIV
* Valerio Valeri, anthropologist
# T. S. R. Prasada Rao

Turaga Sundara Rama Prasada Rao (20 January 1939 – 7 April 2022) was an Indian engineer, known for his contributions in the fields of petroleum refining and heterogeneous catalysis. He was a former director of the Indian Institute of Petroleum and a former deputy general manager of the Indian Petrochemicals Corporation Limited. He was known for his studies in petrochemical engineering; his studies have been documented by way of a number of articles and Google Scholar, an online repository of scientific articles has listed 123 of them. He also co-edited a book, Recent Advances in Basic and Applied Aspects of Industrial Catalysis, published by Elsevier.
Born on 20 January 1939, Rao was an elected fellow of Indian National Academy of Engineering, and the Indian Academy of Sciences. He was also a member of Andhra Pradesh Akademi of Sciences, Indian Institute of Chemical Engineers, and New York Academy of Sciences. He shared the 1996 Om Prakash Bhasin Award for Engineering with M. R. Srinivasan and C. G. Krishnadas Nair. He received the Petrotech Lifetime Achievement Award in 2004. He was also a recipient of several other honors including Chemtech Outstanding Scientist Award, K. G. Naik Gold Medal, FICCI Award Technology Award of the Council of Scientific and Industrial Research.
Rao died in Hyderabad on 7 April 2022, at the age of 83.

## Selected bibliography
### Books

* T.S.R. Prasada Rao; G. Murali Dhar (25 February 1998). Recent Advances in Basic and Applied Aspects of Industrial Catalysis. Elsevier. ISBN 978-0-08-054038-2.

### Articles

* Maity, S.K; Rana, M.S; Srinivas, B.N; Bej, S.K; Murali Dhar, G; Prasada Rao, T.S.R (March 2000). "Characterization and evaluation of ZrO2 supported hydrotreating catalysts". Journal of Molecular Catalysis A: Chemical. 153 (1–2): 121–127. doi:10.1016/s1381-1169(99)00311-8. ISSN 1381-1169.
* Maity, S.K.; Rana, M.S.; Bej, S.K.; Ancheyta-Juárez, J.; Murali Dhar, G.; Prasada Rao, T.S.R. (January 2001). "Studies on physico-chemical characterization and catalysis on high surface area titania supported molybdenum hydrotreating catalysts". Applied Catalysis A: General. 205 (1–2): 215–225. doi:10.1016/s0926-860x(00)00567-6. ISSN 0926-860X.
* Sahoo, S.K.; Viswanadham, N.; Ray, N.; Gupta, J.K.; Singh, I.D. (January 2001). "Studies on acidity, activity and coke deactivation of ZSM-5 during n-heptane aromatization". Applied Catalysis A: General. 205 (1–2): 1–10. doi:10.1016/s0926-860x(00)00543-3. ISSN 0926-860X.
* Rana, M.S.; Srinivas, B.N.; Maity, S.K.; Murali Dhar, G.; Prasada Rao, T.S.R. (October 2000). "Origin of Cracking Functionality of Sulfided (Ni) CoMo/SiO2–ZrO2 Catalysts". Journal of Catalysis. 195 (1): 31–37. doi:10.1006/jcat.2000.2968. ISSN 0021-9517.
* Rana, M.S.; Maity, S.K.; Ancheyta, J.; Dhar, G.Murali; Prasada Rao, T.S.R. (October 2003). "TiO2–SiO2 supported hydrotreating catalysts: physico-chemical characterization and activities". Applied Catalysis A: General. 253 (1): 165–176. doi:10.1016/s0926-860x(03)00502-7. ISSN 0926-860X.
* India portal
* Engineering portal
# Justus, Ohio

Justus is an unincorporated community in Stark County, in the U.S. state of Ohio.

## History

Justus had its start in 1872 when the Wheeling and Lake Erie Railroad was extended to that point. The community was named after William H. Justus, one of the partners of the firm that owned the grain warehouse near the railroad station. A post office called Justus was established in 1874, and remained in operation until 1964.

## Notable people

* Benjamin Franklin Fairless, a steel executive, was raised in Justus.
* George W. Wilhelm (1847–1902), store owner in Justus; Ohio state senator and representative
# Robert Browne (by 1533 – 1565 or later)

Robert Browne (by 1533 – 1565 or later), of Launceston, Cornwall, was an English politician.
He was a Member (MP) of the Parliament of England for Newport, Cornwall in November 1554.
# Simon Thirgood

Simon Jeremy Thirgood (6 December 1962 – 30 August 2009) was a Scottish ecologist and conservationist. He was the author of more than 100 scientific papers on deer, mountain hares and moorland management, birds of prey, and conservation problems, and senior editor of the Journal of Applied Ecology. On 30 August 2009, Thirgood was killed in Ethiopia when the building he was in collapsed.
# 31st Army Corps

31st Army Corps may refer to:
* 31st Army Corps (France)
* 31st Army Corps (Russian Empire)
* 31st Army Corps (Soviet Union)
# 2010–11 EHF Cup Winners' Cup

The 2010–11 EHF Cup Winners' Cup season, VfL Gummersbach won the Europe's club handball tournament.

## Knockout stage
### Round of 16

| Team 1 | Agg.Tooltip Aggregate score | Team 2 | 1st leg | 2nd leg |
| Xico Andebol | 47–78 | VfL Gummersbach | 20–39 | 27–39 |
| Amaya Sport San Antonio | 63–57 | HRK Izvidac | 36–29 | 27–28 |
| Tremblay-en-France Handball | 49–47 | Balatonfüredi KSE | 29–27 | 20–20 |
| Budyvelnik | 47–60 | UCM Sport RESITA | 16–33 | 31–27 |
| Elverum Håndball | 60–58 | HC Kaustik Volgograd | 30–30 | 30–28 |
| RK Kolubara | 53–72 | RK Maribor Branik | 26–40 | 27–32 |
| Moser Medical UHK Krems | 60–64 | HK Drott HALMSTAD | 31–29 | 29–35 |
| RK Vardar PRO | 60–43 | FIF Copenhagen | 33–20 | 27–23 |

### Quarterfinals

| Team 1 | Agg.Tooltip Aggregate score | Team 2 | 1st leg | 2nd leg |
| RK Maribor Branik | 55–69 | Amaya Sport San Antonio | 28–34 | 27–35 |
| VfL Gummersbach | 81–58 | Elverum Håndball | 44–25 | 37–33 |
| RK Vardar PRO | 46–45 | UCM Sport RESITA | 28–22 | 18–23 |
| HK Drott HALMSTAD | 51–53 | Tremblay-en-France Handball | 26–31 | 25–22 |

### Semifinals

| Team 1 | Agg.Tooltip Aggregate score | Team 2 | 1st leg | 2nd leg |
| Amaya Sport San Antonio | 48–48 | Tremblay-en-France Handball | 27–23 | 21–25 |
| VfL Gummersbach | 71–50 | RK Vardar PRO | 33–21 | 38–29 |

### Finals

| Team 1 | Agg.Tooltip Aggregate score | Team 2 | 1st leg | 2nd leg |
| Tremblay-en-France Handball | 54–56 | VfL Gummersbach | 28–30 | 26–26 |
* EHF Cup Winners' Cup 2010–11 Winner
* VfL Gummersbach
# Rushcliffe Wapentake

Rushcliffe was a wapentake (administrative area, equivalent to a hundred) of the historic county of Nottinghamshire, England. It was in the south of the county, on the south side of the River Trent, covering the parishes of Barton in Fabis, Bradmore, Bunny, Clifton with Glapton, Costock, East Leake, Edwalton, Gotham, Keyworth, Kingston on Soar, Normanton on Soar, Plumtree, Ratcliffe on Soar, Rempstone, Ruddington, Stanford on Soar, Stanton-on-the-Wolds, Sutton Bonington, Thorpe in the Glebe, Thrumpton, West Leake, Widmerpool, Wilford, Willoughby on the Wolds and Wysall.
Contained within the boundaries of the wapentake is the western part of the current Rushcliffe Borough and a small area of the City of Nottingham around Clifton.

## Etymology

Rushcliffe means "cliff where brushwood grows", from Old English hris "brushwood" and clif "cliff". The name was recorded as Riselclif in an undated source.
# Jurek (given name)

Jurek is a Polish masculine given name, the most common diminutive form (hypocorism) of Jerzy. It may refer to:
* Jurek Becker (1937–1997), Polish-born German writer, screenwriter and East German dissident
* Jerzy Jurek Dybał (born 1977), Polish conductor and double-bassist
* Jurek Martin (born 1942), British-born journalist
* Jurek Wajdowicz (born 1951), Polish-born American artist, graphic designer, photographer and art director
# Cathedral of St. George (Saskatoon)

The Ukrainian Catholic Cathedral of St. George was designed by architect the Very Reverend Philip Ruh, O.M.I. in 1923. It is located in Pleasant Hill, Core Neighbourhoods SDA, Saskatoon, Saskatchewan, Canada and is the Episcopal See of the Bishop of the Saskatoon Eparchy.

## History

The organizational meeting of the Ukrainian Catholic Parish of St. George took place on September 29, 1912 at which the first Executive was elected. In the same year 40 persons enrolled as members.
Construction of the present church, the second church of the parish, begun in 1939 and was completed in 1943. The church is a massive mason structure which stands on a high concrete basement measures 104 x 90 feet (27 m); the intersecting arms are 30 feet (9.1 m) wide. Its architectural plan is a four column cruciform Byzantine domed basilica with north, south and east apses, and seven domes. The central area of the church is dominated by a large octagonal dome which is reinforced by the arcades of the vaulted ceilings and is supported by four massive octagonal columns. Each side of the octagonal drum supporting the dome has two arched windows which collectively illuminate the dome.
In 1950 to 1955 the icons and artistic decoration of the church were done by Theodore Baran, member of St. George's parish. The Iconostasis was added in 1991.
On various occasions, the cathedral has also been visited by eminent clergy of the Ukrainian and Roman Catholic Churches and other Christian Churches.

## Clergy

Between 1992 and 2010 the parish priest was Rt. Rev. Vladimir Mudri, STL, JCOD. Currently The Parish Priest is Rev. Ivan Nahachewski.
# State Highway 63 (Andhra Pradesh)

State Highway 63 (Andhra Pradesh) is a state highway in the Indian state of Andhra Pradesh

## Route

It starts at Gudivada and passes through Mudinepalle and ends at Bhimavaram.
# Beyond the Border

Beyond the Border may refer to:
* Beyond the Border (1925 film), a 1925 silent film
* Beyond the Border (2011 film), a 2011 Swedish film
* Beyond the Border Storytelling Festival, based in Wales, UK
# Robert Browne (bishop)

Robert Browne (6 November 1844 – 23 March 1935) was an Irish Roman Catholic priest who served as President of Maynooth College and Bishop of Cloyne.

## Life

Robert Browne was born in Charleville, Co. Cork to Robert Browne and Margaret Mullins. He was educated at St. Colman's College, Fermoy in Cork before he pursued clerical studies at St. Patrick's College, Maynooth. Browne was ordained on 18 May 1869 for Cloyne Diocese where he ministered and worked in St. Colman's College in 1870. Rev. Browne returned to Maynooth College in 1874 and became Dean in 1875, vice-President in 1883 and President in 1885 a position he held until he was appointed Bishop of Cloyne in 1894.
During Browne's tenure as president of Maynooth many developments were undertaken such as the completion of the college chapel and exhibition hall. He also served as editor of the "Irish Ecclesiastical Record" until his appointment as Bishop.
His nephew was the Jesuit priest and noted photographer of the Titanic and First World War Francis Browne SJ, whom, since his parents died when he was quite young, Bishop Browne raised and supported, purchasing his first camera and giving him a present of tickets to travel from Southampton to Queenstown (Cobh).
Browne died on 23 May 1935.
# Aimé Leon Meyvis

Aimé Leon Meyvis (1877 in Sint-Gillis-Waas, Flanders – 1932) was a Flemish landscape painter who immigrated to East Rochester, New York in 1902. He became a member of the group known as the Finger Lakes Regional Artists. Meyvis studied at The Royal Academy in The Hague in the Netherlands. He exhibited at the 3rd Exhibition of Contemporary Artists in Washington, D.C., the National Academy of Design, the Pennsylvania Academy of the Fine Arts, The Art Institute of Chicago and the Rochester Art Club. Most of his work was done in oils.
# Desert cockroach

Desert cockroach may refer to:
* Arenivaga investigata, also known as a desert cockroach
* Therea petiveriana, also referred to as a desert cockroach found in southern India
# K. Gopalsamy

K. Gopalsamy is an Indian politician and was a member of the 14th Tamil Nadu Legislative Assembly from the Rajapalayam constituency. He represented the All India Anna Dravida Munnetra Kazhagam party.
The elections of 2016 resulted in his constituency being won by S. Thangappandian. The AIADMK had chosen to field A. A. S. Shyam rather than Gopalsamy.
# Duplication and elimination matrices

In mathematics, especially in linear algebra and matrix theory, the duplication matrix and the elimination matrix are linear transformations used for transforming half-vectorizations of matrices into vectorizations or (respectively) vice versa.

## Duplication matrix

The duplication matrix $D_{n}$ is the unique $n^{2}\times {\frac {n(n+1)}{2}}$ matrix which, for any $n\times n$ symmetric matrix $A$, transforms $\mathrm {vech} (A)$ into $\mathrm {vec} (A)$:
    $D_{n}\mathrm {vech} (A)=\mathrm {vec} (A)$.
For the $2\times 2$ symmetric matrix $A=\left[{\begin{smallmatrix}a&b\\b&d\end{smallmatrix}}\right]$, this transformation reads
    $D_{n}\mathrm {vech} (A)=\mathrm {vec} (A)\implies {\begin{bmatrix}1&0&0\\0&1&0\\0&1&0\\0&0&1\end{bmatrix}}{\begin{bmatrix}a\\b\\d\end{bmatrix}}={\begin{bmatrix}a\\b\\b\\d\end{bmatrix}}$
The explicit formula for calculating the duplication matrix for a $n\times n$ matrix is:
$D_{n}^{T}=\sum \limits _{i\geq j}u_{ij}(\mathrm {vec} T_{ij})^{T}$
Where:
* $u_{ij}$ is a unit vector of order ${\frac {1}{2}}n(n+1)$ having the value $1$ in the position $(j-1)n+i-{\frac {1}{2}}j(j-1)$ and 0 elsewhere;
* $T_{ij}$ is a $n\times n$ matrix with 1 in position $(i,j)$ and $(j,i)$ and zero elsewhere
Here is a C++ function using Armadillo (C++ library):

## Elimination matrix

An elimination matrix $L_{n}$ is a ${\frac {n(n+1)}{2}}\times n^{2}$ matrix which, for any $n\times n$ matrix $A$, transforms $\mathrm {vec} (A)$ into $\mathrm {vech} (A)$:
    $L_{n}\mathrm {vec} (A)=\mathrm {vech} (A)$.
By the explicit (constructive) definition given by Magnus & Neudecker (1980), the ${\frac {1}{2}}n(n+1)$ by $n^{2}$ elimination matrix $L_{n}$ is given by
    $L_{n}=\sum _{i\geq j}u_{ij}\mathrm {vec} (E_{ij})^{T}=\sum _{i\geq j}(u_{ij}\otimes e_{j}^{T}\otimes e_{i}^{T}),$
where $e_{i}$ is a unit vector whose $i$-th element is one and zeros elsewhere, and $E_{ij}=e_{i}e_{j}^{T}$.
Here is a C++ function using Armadillo (C++ library):
For the $2\times 2$ matrix $A=\left[{\begin{smallmatrix}a&b\\c&d\end{smallmatrix}}\right]$, one choice for this transformation is given by
    $L_{n}\mathrm {vec} (A)=\mathrm {vech} (A)\implies {\begin{bmatrix}1&0&0&0\\0&1&0&0\\0&0&0&1\end{bmatrix}}{\begin{bmatrix}a\\c\\b\\d\end{bmatrix}}={\begin{bmatrix}a\\c\\d\end{bmatrix}}$.