Dictionary:Tensor

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A set of functions of the coordinates. A rectangular array of coefficients for a system of linear equations. Concerned with how point functions change with a change in coordinates, that is, how a function transforms into another coordinate system. If a tensor can be expressed in terms of partial derivatives of one coordinate set with respect to another, it is an Einstein-Ricci tensor; for example,

,

where Pni(x) and Pni(y) represent stresses in the x- and y-coordinate systems, respectively. Tensors of identical type are parallel. The norm of a tensor equals the sum of the squares of its components, that is, the square of its magnitude. The scalar product of two tensors equals the sum of the products of corresponding components; it also equals the product of the two magnitudes multiplied by the cosine of the generalized angle between the tensors. Nonzero stress and strain tensors are mutually orthogonal if the corresponding strain-energy density vanishes.