and local rings. It was introduced by Dieudonné (1943). If K is a division ring, then the Dieudonné determinant is a group homomorphism from the group...

MR 0478177 Dieudonné, Jean (1981), Choix d'œuvres mathématiques. Tome I (in French), Paris: Hermann, ISBN 978-2-7056-5922-6, MR 0611149 Dieudonné, Jean (1981)...

Cauchy determinant Cayley–Menger determinant Dieudonné determinant Slater determinant Determinantal conjecture Lang 1985, §VII.1 "Determinants and Volumes"...

and only if it has a nonzero determinant and the eigenvalues of a square matrix are the roots of a polynomial determinant. Matrix theory is the branch...

the vectors are linearly dependent. Dieudonné determinant quasideterminant Moore, E. H. (1922), "On the determinant of an hermitian matrix with quaternionic...

^{*}(2n),} where the determinant is taken on the matrices in C2n. Alternatively, one can define this as the kernel of the Dieudonné determinant G L ( n , H )...

existing determinant analog for noncommutative settings—perhaps the most famous examples are the Dieudonné determinant and quantum determinant. However...

to hold true. There are several modifications of the determinant theory: Dieudonné determinant which takes values in the abelianization K*/[K*, K*] of...

structure to a (semi-)linear-algebraic setting. The basic object is the Dieudonné ring D = W(k){F,V}/(FV − p), which is a quotient of the ring of noncommutative...

left multiplication, then the determinant is an invariant of this action because the determinant of A X equals the determinant of X, when A is in SLn. Let...

group, and denoted SO(n). It consists of all orthogonal matrices of determinant 1. This group is also called the rotation group, generalizing the fact...

all have a determinant whose absolute value is unity. Rotation matrices have a determinant of +1, and reflection matrices have a determinant of −1. The...

generate the orthogonal group, and this result is known as the Cartan–Dieudonné theorem. Similarly the Euclidean group, which consists of all isometries...

Publishers, p. 474, OCLC 505700 See for example Jean Dieudonné, Infinitesimal Calculus, p. 119 or Jean Dieudonné, Calcul Infinitésimal, p.135. Bleistein, N. and...

adjugate matrix divided by its determinant). The method of proof here can be found in the books of Henri Cartan, Jean Dieudonné, Serge Lang, Roger Godement...

Grothendieck, Alexandre; Jean Dieudonné (1964), "Éléments de géométrie algébrique (rédigés avec la collaboration de Jean Dieudonné) : IV. Étude locale des schémas...

determined by a triangulation. There is another approach, expounded in (Dieudonné 1972), which does directly assign a meaning to integration over M, but...

physics. Noether was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and Norbert Wiener as the most important woman in the history...

K[xi,j] in nd indeterminates given by mapping [λ1 λ2 ... λd] to the determinant of the d by d matrix consisting of the columns of the xi,j indexed by...

; Dahourou, H.; Traore, F.; Ouattara, S.; Ouedraogo, O.; Kienou, K.; Dieudonné, Y. Y.; Deneys, V. (2019). "Distribution of ABO and RHD blood group antigens...

(ab)2 is as follows. First of all, (ab) is a shorthand form for the determinant of a matrix whose rows are a1, a2 and b1, b2, so ( a b ) = a 1 b 2 −...

rotation is the composition of two reflections, a special case of the Cartan–Dieudonné theorem. The finite subgroups of S O ( 3 ) {\displaystyle \mathrm {SO}...

Jacobian, Steinerian. -ant Nouns ending in -ant are often invariants, as in determinant, covariant, and so on. -ary Adjectives ending in -ary often refer to...

theorem", Encyclopedia of Mathematics, EMS Press, ISBN 1-4020-0609-8 Dieudonné, Jean (1989). A History of Algebraic and Differential Topology, 1900–1960...

Baer's Linear Algebra and Projective Geometry or Dieudonné's La Géometrie des Groupes Classique. Jean Dieudonné reviewed the book for Mathematical Reviews and...

MR 1563614. Jacobson, N. (1939). "An application of E. H. Moore's determinant of a hermitian matrix". Bull. Amer. Math. Soc. 45 (10): 745–748. doi:10...

mathematicians, including M. G. Krein, William T. Reid, Peter Lax and Jean Dieudonné. Fredholm theory already implies that any element of the spectrum is an...

{\displaystyle |{\textbf {f}}(b)-{\textbf {f}}(a)|} yields the theorem. Jean Dieudonné in his classic treatise Foundations of Modern Analysis discards the mean...

fetalis due to congenital parvovirus B19. This condition was studied as a determinant of later fetal outcomes, such as miscarriage or perinatal death, in 2016...

transformation can be expressed as a composition of reflections (the Cartan–Dieudonné theorem), it follows that this representation of the pin group is a homomorphism...