Two-point tensor
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"Double vector" redirects here. For dual vectors, see dual space. For bivectors, see bivector.
Two-point tensors, or double vectors, are tensor-like quantities which transform as Euclidean vectors with respect to each of their indices. They are used in continuum mechanics to transform between reference ("material") and present ("configuration") coordinates.[1] Examples include the deformation gradient and the first Piola–Kirchhoff stress tensor.
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As with many applications of tensors, Einstein summation notation is frequently used. To clarify this notation, capital indices are often used to indicate reference coordinates and lowercase for present coordinates. Thus, a two-point tensor will have one capital and one lower-case index; for example, AjM.