Examples of 'metric tensor' in a sentence
Meaning of "metric tensor"
metric tensor - In mathematics and physics, a metric tensor is a type of function that takes as input a pair of tangent vectors and returns a scalar quantity. It is used to define the distance between two points in a space
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- a symmetric bilinear form which is non-degenerate (i.e., having all non-zero eigenvalues); a differential of distance on a manifold
How to use "metric tensor" in a sentence
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metric tensor
The metric tensor is an example of a tensor field.
The reciprocal of the metric tensor is simply.
A metric tensor describes the geometry of spacetime.
Where g is the determinant of the metric tensor.
The metric tensor is not a single number.
Instead a weaker condition of nondegeneracy is imposed on the metric tensor.
Thus the metric tensor gives the infinitesimal distance on the manifold.
Contain only first order time derivatives of the metric tensor.
We develop a method of constructing a hybrid metric tensor adapted to color catadioptric images.
The geodesic paths for a spacetime are calculated from the metric tensor.
It is made of the metric tensor and its first and second partial derivatives.
The solutions of the field equations are the components of the metric tensor of spacetime.
Metric tensor is no longer the Kronecker delta.
Special relativity describes spacetime as a manifold whose metric tensor has a negative eigenvalue.
Gab is the Metric tensor which is solution of Einstein equations.
See also
Contravariant indices can be turned into covariant indices by contracting with the metric tensor.
Where η is the Minkowski metric tensor with signature.
The solutions of the EFE are the components of the metric tensor.
The metric tensor is often just called ' the metric.
The equation for this operator requires the inverse of the metric tensor g and its determinant.
A manifold with a metric tensor is called a pseudo-Riemannian manifold.
The family gp of inner products is called a Riemannian metric or Riemannian metric tensor.
The Minkowski metric η is the metric tensor of Minkowski space.
Either the Christoffel symbols or the curvature are calculated from the metric tensor.
A complex spacetime geometry refers to the metric tensor being complex, not spacetime itself.
A higher index can be changed to a lower index by multiplication with the Metric tensor gij.
A metric tensor allows distances along curves to be determined through integration, and thus determines a metric.
We thus build a new Gaussian kernel dependent on the Riemannian metric tensor.
Where the metric tensor measures lengths and angles, the symplectic form measures oriented areas.
In general relativity, the gravitational potential is replaced by the metric tensor.
In Riemannian geometry, the metric tensor is used to define the angle between two tangents.
Orthogonal coordinates never have off-diagonal terms in their metric tensor.
The Inverse Metric tensor is the Tensor gij such that,.
Note that in general, no such relation exists in spaces not endowed with a metric tensor.
Metric tensor First fundamental form Second fundamental form Tautological one-form.
Here a metric (or Riemannian) connection is a connection which preserves the metric tensor.
For two-dimensional maps, a metric tensor has three components.
The most familiar example is that of elementary Euclidean geometry: the two-dimensional Euclidean metric tensor.
This formula for the metric tensor formula 1 is called the Kerr-Newman metric.
Physically, there are a lot of distinct pieces that promote the Metric Tensor in general relativity.
The metric tensor is clearly the 1-dimensional Euclidean metric.
G = Determinant of the matrix gij associated with Metric Tensor g.
Note, Obviously, if a tensor is a metric tensor in a basis, it will be in all.
Here is the absolute value of the determinant of the metric tensor " g " " ij.
Thus the metric tensor is the Kronecker delta δ " ij " in this coordinate system.
In general relativity, the gravitational field is characterized by a symmetric rank-2 tensor, the metric tensor.
The Metric tensor is the Tensor gij of order 2, whose components are gij.
Let V be an n-dimensional vector space, equipped with a metric tensor (of possibly mixed signature).
Where is the metric tensor expressed in Euler angles-a non-orthogonal system of curvilinear coordinates -.
See page 485 regarding determinant of metric tensor.
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Examples of using Metric
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All figures are in metric tonnes per year
This metric is not commonly reported or available
Examples of using Tensor
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The metric tensor is an example of a tensor field
This is similar to the notion of tensor rank
The zero tensor has rank zero
