In contrast to a version of Schur's lemma due to Dixmier, it does not require k to be uncountable.
Schur function | Issai Schur | Michael Schur | lemma | lemma (mathematics) | König's lemma | Zorn's lemma | the lemma that is not Burnside's | Sylvia Schur | Schur's lemma | Schur complement method | Schur | Lemma | Johnson–Lindenstrauss lemma | Hotelling's lemma | Gustav-Adolf Schur | Fundamental lemma of calculus of variations |
The existence of Aronszajn trees (=-Aronszajn trees) was proven by Nachman Aronszajn, and implies that the analogue of König's lemma does not hold for uncountable trees.
Consequently, this lemma is sometimes referred to as the lemma that is not Burnside's.
: a much smaller matrix called the Schur complement of .
Masayoshi Nagata proved in the 1950s that for any commutative local ring A with maximal ideal m there always exists a smallest ring Ah containing A such that Ah is Henselian with respect to mAh.
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Completeness of a ring is not a necessary condition for the ring to have the Henselian property: Goro Azumaya in 1950 defined a commutative local ring satisfying the Henselian property for the maximal ideal m to be a Henselian ring.
Hotelling's lemma: an economic rule relating the supply of a good to the profit of the good's producer
König's lemma (also known as König's infinity lemma), named after Dénes Kőnig
In mathematics, the Lehmer–Schur algorithm (named after Derrick Henry Lehmer and Issai Schur) is a root-finding algorithm extending the idea of enclosing roots like in the one-dimensional bisection method to the complex plane.
Schur collaborated with The Decemberists on their music video for Calamity Song from the album The King Is Dead.
It was Adriano Garsia's idea to construct an appropriate module in order to prove positivity (as was done in his previous joint work with Procesi on Schur positivity of Kostka–Foulkes polynomials).
In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in Cn, the function –log d(z) is plurisubharmonic, where d is the distance to the boundary.
In mathematics, especially in the area of algebra known as module theory, Schanuel's lemma, named after Stephen Schanuel, allows one to compare how far modules depart from being projective.
Henry Scheffé published a proof of the statement on convergence of probability densities in 1947.
Issai Schur (1875–1941), Lithuanian-German-Israeli mathematician
In numerical analysis, the Schur complement method, named after Issai Schur, is the basic and the earliest version of non-overlapping domain decomposition method, also called iterative substructuring.
The first Jacobi-Trudi formula expresses the Schur polynomial as a determinant
This property was named after the early 20th century mathematician Issai Schur who showed that ℓ1 had the above property in his 1921 paper.
The lemma is named after Ronald Shephard who gave a proof using the distance formula in his book Theory of Cost and Production Functions (Princeton University Press, 1953).
Following the death of her husband Saul Schur, just shy of their 50th wedding anniversary, Sylvia Schur married architect Kaneji Domoto, who died in 2002.
Zorn's lemma is a proposition used in many areas of theoretical mathematics.
# Banach's extension theorem which is used to prove one of the most fundamental results in functional analysis, the Hahn–Banach theorem
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It occurs in the proofs of several theorems of crucial importance, for instance the Hahn–Banach theorem in functional analysis, the theorem that every vector space has a basis, Tychonoff's theorem in topology stating that every product of compact spaces is compact, and the theorems in abstract algebra that every nonzero ring has a maximal ideal and that every field has an algebraic closure.