Specht's theorem gives a necessary and sufficient condition for two complex matrices to be unitarily equivalent. It is named after Wilhelm Specht, who...

axis theorem (linear algebra) Rank–nullity theorem (linear algebra) Rouché–Capelli theorem (Linear algebra) Sinkhorn's theorem (matrix theory) Specht's theorem...

equivalent. The spectral theorem says that every normal matrix is unitarily equivalent to some diagonal matrix. Specht's theorem states that two matrices...

Characteristic function Field trace Golden–Thompson inequality Singular trace Specht's theorem Trace class Trace identity Trace inequalities von Neumann's trace inequality...

For simple roots, this results immediately from the implicit function theorem. This is true also for multiple roots, but some care is needed for the...

{b^{2}}{4}}}}.} This formula can also be derived from the Pythagorean theorem using the fact that the altitude bisects the base and partitions the isosceles...

induction theorems give criteria for the surjectivity of this map or closely related ones. Artin's induction theorem is the most elementary theorem in this...

the representation theory of Lie groups, and combinatorics. Cayley's theorem states that every group G {\displaystyle G} is isomorphic to a subgroup...

functions on Young tableau and the resulting representations are called Specht modules which again construct all complex irreducible representations of...

mathematics, categorification is the process of replacing set-theoretic theorems with category-theoretic analogues. Categorification, when done successfully...

cousin of the mathematician Wolfgang Haken, who proved the Four color theorem. He was a nephew of Werner Haken, a doctoral student of Max Planck. After...

K has characteristic equal to zero or greater than n then by Maschke's theorem the group algebra KSn is semisimple. In these cases the irreducible representations...

for the idea and method for his classic 1904 proof of the Well-ordering theorem from an "Axiom of choice", which has become an integral part of modern...

important both in pure and applied mathematics. It enters into proofs of theorems such as the Baker–Campbell–Hausdorff formula, and it is used frequently...

economist, won the Nobel Prize in Economics, developed the impossibility theorem in social choice theory Bruno Augenstein: V.P., physicist, mathematician...

which articulates properties of graphs in algebraic terms, then works out theorems regarding them. In the first section, he tackles the applications of linear...

representation Borel–Weil–Bott theorem Over an algebraically closed field of characteristic zero, the Borel–Weil–Bott theorem realizes an irreducible representation...

Positioning System (GPS) becomes fully operational. Proof of Fermat's Last Theorem is discovered by Andrew Wiles. Construction started in 1998 on the International...

inequality Schur's theorem Schur-convex function Schur–Weyl duality Lehmer–Schur algorithm Schur's property for normed spaces. Jordan–Schur theorem Schur–Zassenhaus...

length, proving an important result now known as the Baik–Deift–Johansson theorem. Their analysis again makes crucial use of the fact that f λ {\displaystyle...

-invariant and cellular w.r.t. i {\displaystyle i} . Tits' deformation theorem for cellular algebras: Let A {\displaystyle A} be a cellular R {\displaystyle...

Council. Isadore Singer, 96, American mathematician (Atiyah–Singer index theorem), Abel Prize winner (2004). Eli Soriano, 73, Filipino televangelist (Ang...

scientist and translator Kenneth Appel (1932–2013), proved four-color theorem Zvi Arad (1942–2018), mathematician Vladimir Arnold (1937–2010), mathematician;...