Tensor Field Function
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A Tensor Field Function is a Tensor-Valued Function that is a Field Function (assigns a tensor to each point of a mathematical space).
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- Counter-Example(s):
- See: Tensor, Vector Field Function, Tensor Matrix, Euclidean Space, Manifold, Differential Geometry, Algebraic Geometry, Strain Tensor, Euclidean Vector.
References
2015
- (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/tensor_field Retrieved:2015-1-18.
- In mathematics, physics, and engineering, a tensor field assigns a tensor to each point of a mathematical space (typically an Euclidean space or manifold). Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in materials, and in numerous applications in the physical sciences and engineering. As a tensor is a generalization of a scalar (a pure number representing a value, like length) and an vector (a geometrical arrow in space), a tensor field is a generalization of a scalar field or vector field that assigns, respectively, a scalar or vector to each point of space.
Many mathematical structures informally called 'tensors' are actually 'tensor fields'. An example is the Riemann curvature tensor.
- In mathematics, physics, and engineering, a tensor field assigns a tensor to each point of a mathematical space (typically an Euclidean space or manifold). Tensor fields are used in differential geometry, algebraic geometry, general relativity, in the analysis of stress and strain in materials, and in numerous applications in the physical sciences and engineering. As a tensor is a generalization of a scalar (a pure number representing a value, like length) and an vector (a geometrical arrow in space), a tensor field is a generalization of a scalar field or vector field that assigns, respectively, a scalar or vector to each point of space.
2009
- (Kolda & Bader, 2009) ⇒ Tamara G. Kolda, and Brett W. Bader. (2009). “Tensor Decompositions and Applications.” In: SIAM review, 51(3). doi:10.1137/07070111X
- ABSTRACT: This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way arrays with [math]\displaystyle{ N \geq 3 }[/math]) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision,