tensor analysis

tensor analysis

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.

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tensor analysis [′ten·sər ə‚nal·ə·səs]

(mathematics)

The abstract study of mathematical objects having components which express properties similar to those of a geometric tensor; this study is fundamental to Riemannian geometry and the structure of Euclidean spaces. Also known as tensor calculus.