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Because of this, if an appropriate coordinate system is chosen, one of the coordinates is ignorable for the physical magnitudes and for themetrictensor.
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In either case, the chosen geometry is specified by its correspondingmetrictensor.
From theCambridge English Corpus
Upon solving this differential equation implicitly using known magnetic field intensities, themetrictensorfor the resulting basis can be computed.
From theCambridge English Corpus
Coordinate systems, in general, are characterized by theirmetrictensor.
From theCambridge English Corpus
The signs in the following tensor analysis depend on the convention used for themetrictensor.
From
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This example is from Wikipedia and may be reused under a CC BY-SA license.Ametrictensordescribes a geometry of spacetime.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Every tensor quantity can be expressed in terms of a frame field, in particular, themetrictensortakes on a particularly convenient form.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The letter "g" with superscripts refers to the inverse of themetrictensor.
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This example is from Wikipedia and may be reused under a CC BY-SA license.This constant would restore to the general theory's description of space-time an invariantmetrictensorfor the fabric of space/existence.
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This example is from Wikipedia and may be reused under a CC BY-SA license.However, the equations can be arranged so that they contain only themetrictensorand not its inverse.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The equation for this operator requires the inverse of themetrictensorg and its determinant.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Further identities can be read off directly from the gamma matrix identities by replacing themetrictensorwith inner products.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The reverse is possible by contracting with the (matrix) inverse of themetrictensor.
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This example is from Wikipedia and may be reused under a CC BY-SA license.By integration, themetrictensorallows one to define and compute the length of curves on the manifold.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Solving the equation for the geometry of space warped due to the mass distribution gives themetrictensor.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The essential motivation for introducing harmonic coordinate systems is that themetrictensoris especially smooth when written in these coordinate systems.
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This example is from Wikipedia and may be reused under a CC BY-SA license.It is defined even in the absence of ametrictensor.
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This example is from Wikipedia and may be reused under a CC BY-SA license.We find the world line that lies on the surface of the sphere of radius r by varying themetrictensor.
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This example is from Wikipedia and may be reused under a CC BY-SA license.This assumption is expressed in differential geometry using ametrictensorthat has a negative coefficient.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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