dimension theorem
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Dimension theorem for vector spaces — In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite, or given by an infinite cardinal number, and defines the dimension of the space.… … Wikipedia
Dimension (vector space) — In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V. It is sometimes called Hamel dimension or algebraic dimension to distinguish it from other types of dimension. This description… … Wikipedia
Théorème de la dimension pour les espaces vectoriels — En mathématiques, le théorème de la dimension pour les espaces vectoriels énonce que deux bases quelconques d un même espace vectoriel ont même cardinalité. Joint au théorème de la base incomplète qui assure l existence de bases, il permet de… … Wikipédia en Français
Atiyah–Singer index theorem — In the mathematics of manifolds and differential operators, the Atiyah–Singer index theorem states that for an elliptic differential operator on a compact manifold, the analytical index (closely related to the dimension of the space of solutions) … Wikipedia
Hausdorff dimension — In mathematics, the Hausdorff dimension (also known as the Hausdorff–Besicovitch dimension) is an extended non negative real number associated to any metric space. The Hausdoff dimension generalizes the notion of the dimension of a real vector… … Wikipedia
Desargues' theorem — Perspective triangles. Corresponding sides of the triangles, when extended, meet at points on a line called the axis of perspectivity. The lines which run through corresponding vertices on the triangles meet at a point called the center of… … Wikipedia
Riemann–Roch theorem — In mathematics, specifically in complex analysis and algebraic geometry, the Riemann–Roch theorem is an important tool in the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates… … Wikipedia
Dilworth's theorem — In mathematics, in the areas of order theory and combinatorics, Dilworth s theorem characterizes the width of any finite partially ordered set in terms of a partition of the order into a minimum number of chains. It is named for the mathematician … Wikipedia
Dvoretzky's theorem — In mathematics, in the theory of Banach spaces, Dvoretzky s theorem is an important structural theorem proved by Aryeh Dvoretzky in the early 1960s.[1] It answered a question of Alexander Grothendieck. A new proof found by Vitali Milman in the… … Wikipedia
Mostow rigidity theorem — In mathematics, Mostow s rigidity theorem, or strong rigidity theorem, or Mostow–Prasad rigidity theorem, essentially states that the geometry of a finite volume hyperbolic manifold of dimension greater than two is determined by the fundamental… … Wikipedia
Rokhlin's theorem — In 4 dimensional topology, a branch of mathematics, Rokhlin s theorem states that if a smooth, compact 4 manifold M has a spin structure (or, equivalently, the second Stiefel Whitney class w 2( M ) vanishes), then the signature of its… … Wikipedia
