In mathematics, a Sylvester domain, named after James Joseph Sylvester by Dicks & Sontag (1978), is a ring in which Sylvester's law of nullity holds. This means that if A is an m by n matrix, and B is an n by s matrix over R, then
ρ(AB) ≥ ρ(A) + ρ(B) – n
where ρ is the inner rank of a matrix. The inner rank of an m by n matrix is the smallest integer r such that the matrix is a product of an m by r matrix and an r by n matrix.
Sylvester (1884) showed that fields satisfy Sylvester's law of nullity and are, therefore, Sylvester domains.
In mathematics, a Sylvesterdomain, named after James Joseph Sylvester by Dicks & Sontag (1978), is a ring in which Sylvester's law of nullity holds....
positive-definite Hermitian matrices. Sylvesterdomain. The Sylvester matrix for two polynomials. Sylvester's sequence, where each term is the product...
James Joseph Sylvester FRS HonFRSE (3 September 1814 – 15 March 1897) was an English mathematician. He made fundamental contributions to matrix theory...
Pope Sylvester I (also Silvester, 285 – 31 December 335) was the bishop of Rome from 31 January 314 until his death on 31 December 335. He filled the...
divisor (in case of coefficients in an integral domain). Sylvester matrices are named after James Joseph Sylvester. Formally, let p and q be two nonzero polynomials...
George Sylvester Viereck (December 31, 1884 – March 18, 1962) was a German-American poet, writer, and pro-German propagandist. He worked on behalf of...
constructed by taking grading into account. Sylvesterdomain A Sylvesterdomain is a ring in which Sylvester's law of nullity holds. tensor The tensor product...
incorporates public domain material from the 1886 Yale Obituary Record. Works by or about Henry Sylvester Cornwell at Internet Archive Henry Sylvester Cornwell at...
public domain in 2024. Sound recordings that were published in 1923 enter the public domain. The most famous work to enter the public domain in the United...
Josuah Sylvester (1563 – 28 September 1618) was an English poet. Sylvester was the son of a Kentish clothier. In his tenth year he was sent to school...
Sylvester Graham (July 5, 1794 – September 11, 1851) was an American Presbyterian minister and dietary reformer known for his emphasis on vegetarianism...
Euploea sylvester, the double-branded crow, also known as the two-brand crow in Australia, is a butterfly found in South Asia, Southeast Asia and parts...
§5.4). Semifirs have invariant basis number and every semifir is a Sylvesterdomain. Cohn, P. M. (1971), "Free ideal rings and free products of rings"...
Hominum Mentes, reformed and renamed the order as the Order of Saint Sylvester and the Golden Militia. He withdrew all faculties to whom and by whomsoever...
Sylvester Maxwell (April 16, 1775 – December 21, 1858) was an American lawyer and legislator. He was son of Hugh Maxwell, and was born April 16, 1775...
Sylvester Mazzolini, in Italian Silvestro Mazzolini da Prierio, in Latin Sylvester Prierias (1456/1457–1527), was a theologian born at Priero, Piedmont;...
Charles Edward Louis John Sylvester Maria Casimir Stuart (31 December 1720 – 30 January 1788) was the elder son of James Francis Edward Stuart making...
including Taz-Mania (1991, starring Taz) and The Sylvester & Tweety Mysteries (1995, starring Sylvester, Tweety, and Granny). The gang also made frequent...
Sylvester Marsh (September 30, 1803, Campton, New Hampshire – December 30, 1884, Concord, New Hampshire) was an American engineer who designed and built...
front-runners for the role, tweeted his joy at the casting. Fellow Scot Sylvester McCoy, who portrayed the Seventh Doctor, tweeted his pleasure over another...
scholar and mathematician Gerbert d'Aurillac (future pope under the name of Sylvester II) studied in Vic and Ripoll and knowledge of mathematics and astronomy...
its Applications vol 57 Cohn, P. M. (2000). "From Hermite rings to Sylvesterdomains". Proc. Amer. Math. Soc. 128 (7): 1899–1904. doi:10.1090/s0002-9939-99-05189-8...
this source, which is in the public domain. This article incorporates text from a publication now in the public domain: Edwin Burton (1913). "Silvester...
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