tensor analysis

tensor analysis
the branch of mathematics dealing with the calculus of tensors, esp. the study of properties that are unaffected by a change of coordinate system.

* * *

Branch of mathematics concerned with relations or laws that remain valid regardless of the coordinate system used to specify the quantities.

Tensors, invented as an extension of vectors, are essential to the study of manifolds. Every vector is a tensor, but tensors are more general and not easily pictured as geometrical objects. A tensor can be thought of as an abstract object defined as a set of components (like geometric coordinates) that, under a transformation of coordinates, undergo a specific type of transformation. While tensors were explored before Albert Einstein, the success of his general theory of relativity led to their widespread exploration and use by mathematicians and physicists.

* * *


Universalium. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • tensor analysis — tenzorinė analizė statusas T sritis fizika atitikmenys: angl. tensor analysis vok. Tensoranalyse, f rus. тензорный анализ, m pranc. analyse tensorielle, f …   Fizikos terminų žodynas

  • tensor analysis — the branch of mathematics dealing with the calculus of tensors, esp. the study of properties that are unaffected by a change of coordinate system …   Useful english dictionary

  • Tensor — For other uses, see Tensor (disambiguation). Note that in common usage, the term tensor is also used to refer to a tensor field. Stress, a second order tensor. The tensor s components, in a three dimensional Cartesian coordinate system, form the… …   Wikipedia

  • analysis — /euh nal euh sis/, n., pl. analyses / seez /. 1. the separating of any material or abstract entity into its constituent elements (opposed to synthesis). 2. this process as a method of studying the nature of something or of determining its… …   Universalium

  • Tensor contraction — In multilinear algebra, a tensor contraction is an operation on one or more tensors that arises from the natural pairing of a finite dimensional vector space and its dual. In components, it is expressed as a sum of products of scalar components… …   Wikipedia

  • Tensor — Levi Civita Symbol im Dreidimensionalen als Beispiel eines besonders einfachen dreistufigen Tensors Der Tensor ist ein mathematisches Objekt aus der Algebra und Differentialgeometrie. Der Begriff wurde ursprünglich in der Physik eingeführt und… …   Deutsch Wikipedia

  • Tensor product of fields — In abstract algebra, the theory of fields lacks a direct product: the direct product of two fields, considered as a ring is never itself a field. On the other hand it is often required to join two fields K and L, either in cases where K and L are …   Wikipedia

  • Tensor field — In mathematics, physics and engineering, a tensor field is a very general concept of variable geometric quantity. It is used in differential geometry and the theory of manifolds, in algebraic geometry, in general relativity, in the analysis of… …   Wikipedia

  • Kovarianter Tensor — Dieser Artikel erläutert den mathematischen Begriff Tensor, die Muskeln werden unter Musculus tensor fasciae antebrachii, Musculus tensor fasciae latae, Musculus tensor tympani und Musculus tensor veli palatini erläutert. Dieser Artikel wurde auf …   Deutsch Wikipedia

  • Dimensional analysis — In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions (usually mass,… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”