OpenLLM-France/wikimedia huggingface dataset:
# Spectrum of a matrix

In mathematics, the spectrum of a matrix is the set of its eigenvalues. More generally, if $T\colon V\to V$ is a linear operator on any finite-dimensional vector space, its spectrum is the set of scalars $\lambda$ such that $T-\lambda I$ is not invertible. The determinant of the matrix equals the product of its eigenvalues. Similarly, the trace of the matrix equals the sum of its eigenvalues. From this point of view, we can define the pseudo-determinant for a singular matrix to be the product of its nonzero eigenvalues (the density of multivariate normal distribution will need this quantity).
In many applications, such as PageRank, one is interested in the dominant eigenvalue, i.e. that which is largest in absolute value. In other applications, the smallest eigenvalue is important, but in general, the whole spectrum provides valuable information about a matrix.

## Definition

Let V be a finite-dimensional vector space over some field K and suppose T : V → V is a linear map. The spectrum of T, denoted σ$_T$, is the multiset of roots of the characteristic polynomial of T. Thus the elements of the spectrum are precisely the eigenvalues of T, and the multiplicity of an eigenvalue λ in the spectrum equals the dimension of the generalized eigenspace of T for λ (also called the algebraic multiplicity of λ).
Now, fix a basis B of V over K and suppose M ∈ Mat$_K$(V) is a matrix. Define the linear map T : V → V pointwise by Tx = Mx, where on the right-hand side x is interpreted as a column vector and M acts on x by matrix multiplication. We now say that x ∈ V is an eigenvector of M if x is an eigenvector of T. Similarly, λ ∈ K is an eigenvalue of M if it is an eigenvalue of T, and with the same multiplicity, and the spectrum of M, written σ$_M$, is the multiset of all such eigenvalues.

## Related notions

The eigendecomposition (or spectral decomposition) of a diagonalizable matrix is a decomposition of a diagonalizable matrix into a specific canonical form whereby the matrix is represented in terms of its eigenvalues and eigenvectors.
The spectral radius of a square matrix is the largest absolute value of its eigenvalues. In spectral theory, the spectral radius of a bounded linear operator is the supremum of the absolute values of the elements in the spectrum of that operator.
# Spilarctia irina

Spilarctia irina is a moth in the family Erebidae. It was described by Vladimir Viktorovitch Dubatolov in 2006. It is found in western Indonesia.
# Spækhugger

Spækhugger (lit. Killer Whale) is a 7.44-metre (24.4 ft) sailboat class designed by Peter Bruun and built in about 500 copies.

## History

The Spækhugger was designed in 1969 for cruising and racing and become the most popular boat in Denmark during the 1970s.
# Manuel Antonio de Jesús Alvarado

Manuel Antonio de Jesus Alvarado (1919-2011) was a musician, conductor and music educator born in Guatemala. He studied harmony, composing and conducting and graduated as a cellist from the Guatemala National Music Conservatoire and received a master's in musical education (?) from the Royal Manchester College of Music. In 1970 he founded the Guatemala Youth Symphony, which he led until its dissolution in 2000. He was awarded the Francisco Marroquin Order from the government of Guatemala for his lifelong dedication to music education.
# Vegard Arnhoff

Vegard Arnhoff (born 7 October 1977) is a Norwegian sailor. He was born in Oslo, and represented the Soon Yacht Club. He competed at the 2000 Summer Olympics in Sydney, where he placed 13th in the 49er class, together with Christoffer Sundby.
# Microphysa (disambiguation)

Microphysa may refer to:
* Microphysa Schrenk, a genus of plants in the family Rubiaceae
* Microphysa Naudin, a genus of plants in the family Melastomataceae, synonym of Miconia
* Microphysa Guenée, a genus of butterflies in the family Erebidae, synonym of Eublemma
* Microphysa E. von Martens, a genus of gastropods in the family Sagdidae, synonym of Hojeda
# Mnesiloba cauditornata

Mnesiloba cauditornata is a moth in the family Geometridae. It is found in New Guinea.
# Richard Brady

Richard Brady, O.F.M. (died 1607) was an Irish prelate of the Roman Catholic Church who served as Bishop of Ardagh from 1576 to 1580 and then Bishop of Kilmore from 1580 to 1607.
A Franciscan friar, he was appointed the Bishop of Ardagh by Pope Gregory XIII on 23 January 1576. Four years later, Brady was translated to the bishopric of Kilmore on 9 March 1580. He held the honours (temporalities) of the Church of Ireland See of Kilmore until they were deprived by Sir John Perrot, Lord Deputy of Ireland in 1585.
He died in September 1607, and was buried in the cloister of Multifernan Abbey, about 6 miles (9.7 km) north of Mullingar, Westmeath.
# Made in Space (album)

Made in Space is an album released by songwriter Francis Dunnery. It was released in 2011 and is his seventh album of new material. It is a departure from his previous records in that it features many elements more akin to contemporary R&B music, alongside his pop songwriting sensibility.

## Track listing

* "Moonflower"
* "Picked You Up and Now I Can't Let You Go"
* "Little Tears from a Big Pair of Brown Eyes"
* "Made in Space"
* "You Make the World Bow Down"
* "Ford and the Dreamers"
* "Bat Thing"
* "Fire on the Plane"
* "Haunted"
* "Seventeen Fires of Love"
# Osmotic stress technique

The osmotic stress technique is a method for measuring the effect of water on biological molecules, particularly enzymes. Just as the properties of molecules can depend on the presence of salts, pH, and temperature, they can depend significantly on the amount of water present. In the osmotic stress technique, flexible neutral polymers such as polyethylene glycol and dextran are added to the solution containing the molecule of interest, replacing a significant part of the water. The amount of water replaced is characterized by the chemical activity of water.
# Providence Presbyterian Church of Bustleton

Providence Presbyterian Church of Bustleton is an historic church in the Bustleton section of Florence Township, Burlington County, New Jersey, United States.
It was built in 1863 and added to the National Register of Historic Places in 1988.
# Mike Castonguay

Mike Castonguay is a music producer, musician and songwriter based in Los Angeles, California.
From 2001 to 2004 Mike worked as a producer, songwriter and musical director for Natural (Sony/BMG), an Orlando, Florida–based band led by the boy band mogul Lou Pearlman. Mike produced numerous songs for the band's two albums Keep It Natural and It's Only Natural. He also produced and co-wrote two singles for the band, "Paradise" and "Let Me Just Fly". The song "Paradise" was featured in the German trailer for the Academy Award Winning film Spirited Away (Disney). He also produced Natural's version of the song Cherish for the Kool & The Gang tribute album The Hits: Reloaded.
In 2005, Mike and former Natural member Michael Johnson formed the band Lukewarm Freeda. Mike was the lead singer and the guitarist for the band.
In 2006, Mike played bass in the band In For The Kill featuring Bill Gaal from the band Nothingface.
From 2006 to 2009 Mike played bass for Evan Taubenfeld as a member of his band The Blacklist Club (Sire/Warner Bros.). The band also featured Devin Bronson and Isaac Carpenter. Mike played bass on Evan's debut album Welcome to the Blacklist Club which also featured Avril Lavigne. Songs from the album appeared on MTV's The Hills, as well as The Sims 3 video game.
Separate from the band, Mike and Evan wrote and produced the theme song for the MTV show Pageant Place which was executive produced by Donald Trump. They also worked together on the MTV show Kaya, the film Lock and Roll Forever (Sony Pictures), the Tyga album No Introduction (Universal), and the Cartoon Network show Props.
Mike has produced and composed music in commercials for Apple, Sprint, VISA and Hidden Valley Ranch while working for the music house Mophonics, in Venice, California. While at Mophonics, he was also an engineer and musician for the film Bella (Lion's Gate).
Mike has also produced and/or written songs featured on The Originals, Pawn Stars, The Real World, Friday Night Lights, NY Ink', The Clockwork Girl, Jane By Design, Last Call with Carson Daly, Best Week Ever', Counting Cars, Tosh.0, Veronica Mars, I'm Through With White Girls and CMT Hot 20 Countdown.
In 2012, Mike produced the vocals and mixed the Season 2 theme song for the TV Land sitcom The Exes.
Mike has also worked with Fastball, Stephen Bishop, Sarah Connor, Kay Hanley, Liberty DeVitto, W. G. Snuffy Walden, Barry Goudreau, Rich Cronin, Robert Carranza, Phil X, Marc Terenzi, Capra, Kelly Blatz, Sacha Sacket, TL Forsberg and many others.
# Milagros de amor

Milagros de Amor ("Miracles of Love") is a Colombian telenovela first aired in 2002. It stars Maritza Rodríguez, Gregorio Pernía, Edmundo Troya and Carlos Humberto Camacho, and ran for 80 episodes.

## Cast

* Maritza Rodríguez as Milagros Viuda de Amor
* Gregorio Pernía as Miguel Abril / Emilio Luna
* Edmundo Troya as Vladimiro Peralta Jr.
* Carlos Humberto Camacho as Hernan 'Raton'
* Carolina Lizarazo as Xiomara Corrales
* Helena Mallarino as Virginia
* Vannesa Blandon as Natalia Amor
* Gloria Gómez as Ofelia
* Julio Medina as Vladimiro Peralta
* Carolina Sarmiento as Magaly 'Negra'
* César Mora as Cayetano
* Ana María Arango as Betsabe
* Gustavo Ángel
* Paola Diaz as Nelly
* Luis Fernando Ardila
* Diego León Hoyos
* Patricia Polanco as Esther de Corrales
* Jorge Cárdenas
* Marcela Vanegas
* Pilar Álvarez
* Geoffrey Deakin as Frank Hannsen
* María Elena Döehring as Catalina Pizarro de Hannsen
* Freddy Flórez as Fabrizio
* Lina María Luna
* Andrea Quejuán as Magdalena
* Jaider Villa as Camilo Pizarro
* Maria Alejandra Lopez
# Milagros del Corral

Milagros del Corral Beltrán (born 1945, Madrid) is a Spanish librarian. She was Director-General of the Biblioteca Nacional de España (National Library of Spain).
In addition to her position as Director-General of the National Library of Spain (September 2007-April 2010), she has served as the State Librarian (Spain), Secretary General of the Spanish Federation of Publishers (1983-1990), and Deputy Assistant Director-General for Culture at UNESCO Headquarters in Paris (1990-2005).

## Awards

* Awarded in 1980 by HM King Juan Carlos I of Spain as a Commander of the Order of Civil Merit (first woman in that range of the Order).
* Honorary Member of the American Institute of Copyright, the Committee Hyoge-Kobe Japan, from Aid to Artisans United States .
* Nationality Colombian honorable
* Honorary Citizen of Popayan, Colombia
* ARDE 2010 Award for best digital leadership (2010) (Spain)
# Mike Pringle (politician)

Mike Pringle (born 25 December 1945) is a Scottish Liberal Democrat politician. He was the Member of the Scottish Parliament (MSP) for Edinburgh South from 2003 to 2011.

## Background

He was born in Northern Rhodesia (modern-day Zambia), and educated at Edinburgh Academy. He is a keen follower of Heart of Midlothian F.C. and was a strong supporter of the campaign to prevent the sale of the club's Tynecastle stadium in 2004. He is a strong supporter of the Free Tibet Campaign and has introduced a Bill into the Scottish Parliament to introduce a levy on plastic bags in Scotland similar to the successful Irish plastic bag tax. He has been an Honorary Vice-president of English-Speaking Union Scotland.

## Political career

From 1992 to 2003 he was a member of the City of Edinburgh Council. In the 1997 UK general election he ran unsuccessfully as a candidate in Edinburgh South, and in the equivalent constituency in the 1999 Scottish Parliament election. In the latter he came third out of the five candidates, with 22% of the vote; less than five hundred votes behind Margo MacDonald. He was also a candidate for the Lothians, but was not elected through the list system.
He ran again in the 2003 Scottish Parliamentary election for Edinburgh South, winning it from Angus MacKay by half a per cent of the votes – a majority of 158. He served on the Justice Committees of the Scottish Parliament.
In September 2006, the Scottish Parliament's Standards Committee banned him for a week from attending full sessions and committee meetings of the Parliament for leaking details of the Shirley McKie case to a newspaper.
He was re-elected in the 2007 Scottish Parliament election.
He lost the redrawn seat of Edinburgh Southern to the SNP's Jim Eadie in the 2011 Scottish Parliament election.
# Mike Salay

Mike Salay (born Michael Szalai; June 10, 1909 – November 19, 1973) was an American racecar driver from South Bend, Indiana. Salay made eight starts in AAA Championship Car in 1948 and 1949 including the 1948 Indianapolis 500. He attempted to qualify again in 1949 but failed to do so. His best finish was sixth at Trenton Speedway in 1949. In 1950 he attempted the June Milwaukee Mile race and failed to qualify. He entered the 1951 Indianapolis 500 but wrecked his car in a practice crash.

## Indy 500 results

| Year | Car | Start | Qual | Rank | Finish | Laps | Led | Retired |
| 1948 | 86 | 31 | 123.393 | 24 | 30 | 3 | 0 | Stalled |
| Totals | Totals | Totals | Totals | Totals | Totals | 3 | 0 | |
| Starts | 1 |
| Poles | 0 |
| Front Row | 0 |
| Wins | 0 |
| Top 5 | 0 |
| Top 10 | 0 |
| Retired | 1 |
# Milan Blagojevic

Milan Blagojević may refer to:
* Milan Blagojevic (soccer) (born 1969), Australian football player
* Milan Blagojević (basketball) (born 1929), Serbian basketball player
* Milan Blagojević Španac (1905–1941), Yugoslav military officer
** Milan Blagojević - Namenska, Serbian chemical defense company
* Milan Blagojevic (jurist) (born 1965), Serbian jurist
# Millepora complanata

Millepora complanata, commonly known as blade fire coral, is a species of fire coral in the family Milleporidae. It is found in shallow waters in the Caribbean Sea where it is a common species. The International Union for Conservation of Nature has assessed its conservation status as being critically endangered.

## Description

Fire corals are colonial coral-like organisms that secrete calcareous skeletons. Colonies of Millepora complanata have an encrusting base and thin upright plates or blades growing to a height of about 50 centimetres (20 in). The plates of Millepora complanata grow perpendicular to the current direction, with some colonies not growing larger than the encrusted base if the current is too strong. The surface of the blades is smooth and the outer margins irregular, with many stumpy protrusions. This fire coral is pale brown or cream coloured, with white tips to the blades. The feeding and defensive polyps are hair-like and project through fine pores on the surface of the blades. Contact with this fire coral by bare skin can cause a severe stinging sensation.

## Distribution and habitat

Millepora complanata has a widespread distribution in the Caribbean Sea. It often grows in areas with vigorous water movement and turbid waters, and is tolerant of siltation.

## Biology

Some of the polyps of Millepora complanata are dactylozooids with hair-like processes and stinging cells that detect the presence of zooplankton and help entrap it. The nematocyst in the dactylozooid is discharged and injects venom into the prey, all within three milliseconds. Other polyps are gastrozooids and their chief function is the ingestion of food for the colony. Copepods form the main part of the diet. The soft tissues of M. complanata contain zooxanthellae, symbiotic photosynthetic dinoflagellates. These provide much of the organic carbon needed by the fire coral. The M. complanata can feed during both day and night, but tend to feed mostly at night.
The reproduction of fire corals is complex and involves an alternation of asexual and sexual generations. The encrusting parts of the coral expand by the growth of stolons, and the edges of blades expand by sympodial growth. Sexual reproduction involves a sessile polyploid stage and the budding off of planktonic medusae. Broken off fragments of coral blades can successfully reattach to the substrate and M. complanata is one of the first coral species to recolonise damaged reefs.
Millepora complanata is susceptible to coral bleaching, a process by which stressed corals expel their zooxanthellae and turn white. In a mass bleaching event in the Caribbean in 1998 caused by thermal stress, both M. complanata and the closely related Millepora alcicornis were affected but M. alcicornis more severely so. Many colonies were killed but some, especially colonies of M. complanata, recovered and regained their colour over the course of a few months.
# Millepora boschmai

Millepora boschmai is a critically endangered species of fire coral. It was previously catalogued in two protected areas in Panama, the Coiba National Park and the Golfo de Chiriquí National Park.
This species was typically found in upper, forereef slopes to deep sand and rubble slopes but they were most abundant at the reef base and deeper outer slopes.
# Mimostedes trivittipennis

Mimostedes trivittipennis is a species of beetle in the family Cerambycidae. It was described by Breuning in 1956.
# Mimostenellipsis pilosa

Mimostenellipsis pilosa is a species of beetle in the family Cerambycidae. It was described by Breuning in 1963.
# Miller's striped mouse

Miller's striped mouse or the Liberian forest hybomys (Hybomys planifrons) is a species of rodent in the family Muridae. It is found in Ivory Coast, Guinea, Liberia, and Sierra Leone. Its natural habitats are subtropical or tropical dry forest, subtropical or tropical moist lowland forest, and subtropical or tropical moist montane forest.
# Miller's rule (optics)

In optics, Miller's rule is an empirical rule which gives an estimate of the order of magnitude of the nonlinear coefficient.
More formally, it states that the coefficient of the second order electric susceptibility response ($\chi _{\text{2}}$) is proportional to the product of the first-order susceptibilities ($\chi _{\text{1}}$) at the three frequencies which $\chi _{\text{2}}$ is dependent upon. The proportionality coefficient is known as Miller's coefficient $\delta$.

## Definition

The first order susceptibility response is given by: $\chi _{1}(\omega )={\frac {Nq^{2}}{m\varepsilon _{0}}}{\frac {1}{\omega _{0}^{2}-\omega ^{2}-{\tfrac {i\omega }{\tau }}}}$
where:
* $\omega$ is the frequency of oscillation of the electric field;
* $\chi _{1}$ is the first order electric susceptibility, as a function of $\omega$;
* N is the number density of oscillating charge carriers (electrons);
* q is the fundamental charge;
* m is the mass of the oscillating charges, the electron mass;
* $\varepsilon _{0}$ is the electric permittivity of free space;
* i is the imaginary unit;
* $\tau$ is the free carrier relaxation time;
For simplicity, we can define $D(\omega )$, and hence rewrite $\chi _{1}$: $D(\omega )=\omega _{0}^{2}-\omega ^{2}-{\tfrac {i\omega }{\tau }}$ $\chi _{1}(\omega )={\frac {Nq^{2}}{\varepsilon _{0}m}}{\frac {1}{D(\omega )}}$
The second order susceptibility response is given by: $\chi _{2}(2\omega )={\frac {Nq^{3}\zeta _{2}}{\varepsilon _{0}m^{2}}}{\frac {1}{D(2\omega )D(\omega )^{2}}}$ where $\zeta _{2}$ is the first anharmonicity coefficient. It is easy to show that we can thus express $\chi _{2}$ in terms of a product of $\chi _{1}$ $\chi _{2}(2\omega )={\frac {\varepsilon _{0}^{2}m\zeta _{2}}{N^{2}q^{3}}}\chi _{1}(\omega )\chi _{1}(\omega )\chi _{1}(2\omega )$
The constant of proportionality between $\chi _{2}$ and the product of $\chi _{1}$ at three different frequencies is Miller's coefficient: $\delta ={\frac {\varepsilon _{0}^{2}m\zeta _{2}}{N^{2}q^{3}}}$
# Miller's rule

Miller's rule or Miller rule may refer to:
* Miller's Rule (optics), an empirical rule which gives an estimate of the order of magnitude of the nonlinear coefficient
* Miller's rules, a set of rules in stellation
* Miller twist rule, a mathematical formula created by Don Miller to calculate the optimum rate of twist for a given bullet traveling through a rifled barrel
* Miller Rule or The Miller test, the United States Supreme Court's test for determining whether speech or expression can be labeled obscene
# Miles Davis Quartet (album)

Miles Davis Quartet (PRLP 161) is a 10 inch LP album by Miles Davis, released in 1954 by Prestige Records. The first four tracks that comprise Side 1 were recorded at New York's WOR Studios, on May 19, 1953. The last three, heard on Side 2, were recorded nearly a year later, at New York's Beltone Studios, on March 15, 1954.
The May 19, 1953 session features bassist and composer Charles Mingus on one track, playing piano. This was to be Davis' final studio session until he finally kicked his heroin habit for good nearly a year later.
The March 15, 1954 session Davis was the second of two Davis recorded immediately after successfully quitting his heroin habit. He used exactly the same quartet he had also recorded with seven days earlier for his third Blue Note session, released as Miles Davis Volume 3 (BLP 5040). Davis says in his autobiography that he arranged the two sessions quickly after returning to New York, as he needed money fast, and both Blue Note's Alfred Lion and Prestige's Bob Weinstock had given him a fair chance earlier when his reputation was in decline. This was the beginning of a new three-year contract with Prestige, which Davis would still be committed to when he signed a better deal with Columbia at the end of 1955.
After the 10" LP format was discontinued, the seven tracks were all included on the 12" album Blue Haze (PRLP 7054).
A vinyl reissue of the album in ten inch format was released for Record Store Day Black Friday, November 25, 2011.

## Personnel

* Miles Davis – trumpet
* John Lewis – piano (Side one, 1–3)
* Charles Mingus – piano (Side one, 4)
* Horace Silver – piano (Side two)
* Percy Heath – bass
* Max Roach – drums (Side one)
* Art Blakey – drums (Side two)
# Mineral Mountains (Arizona)

The Mineral Mountains are a group of rugged, volcanic hills and mountains southwest of Superior and northeast of Florence in Pinal County, Arizona.
The White Canyon Wilderness Area is in the eastern portion of this range.
# Milyutinsky

Milyutinsky (masculine), Milyutinskaya (feminine), or Milyutinskoye (neuter) may refer to:
* Milyutinsky District, a district of Rostov Oblast, Russia
* Milyutinsky (rural locality), a rural locality (a khutor) in Krasnodar Krai, Russia
* Milyutinskaya, a rural locality (a stanitsa) in Rostov Oblast, Russia