What is a browser.
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Relax dude, not everyone is a computer expert or even needs to be.
What's a balance shaft?
And people wonder why I get upset at drivers sometimes.
What's a balance shaft?
And people wonder why I get upset at drivers sometimes.
Boom. It's hard to remember that most people are like this. The women in my life still double click links. :cool2:
Can any of you tell me what a covariant tensor in pseudo-Euclidian Minkowski spacetime is? No? Fucking noobs.
The above figure illustrates how the contravariant and covariant representations would be plotted in terms of components on a 2D curvilinear non-orthogonal grid for a generic vector A. Note that the sum of either pair of vectors yields the same vector. Also note that the covariant basis vectors are parallel to their respective coordinate lines while the contravariant basis vectors are orthogonal to the directions of the other coordinate lines.
The above figure illustrates how the contravariant and covariant representations would be plotted in terms of components on a 2D curvilinear non-orthogonal grid for a generic vector A. Note that the sum of either pair of vectors yields the same vector. Also note that the covariant basis vectors are parallel to their respective coordinate lines while the contravariant basis vectors are orthogonal to the directions of the other coordinate lines.
Hurr...
The above figure illustrates how the contravariant and covariant representations would be plotted in terms of components on a 2D curvilinear non-orthogonal grid for a generic vector A. Note that the sum of either pair of vectors yields the same vector. Also note that the covariant basis vectors are parallel to their respective coordinate lines while the contravariant basis vectors are orthogonal to the directions of the other coordinate lines.
Your comparision is out of line. people don't use tensors on daily basis. It would be like asking them - what programming language is chrome written on.
Smarts here are measured in these $$$. Rank and bank. Sling dem berries. If you want to show off how big your brain is, go find a science forum where you can compete with people who give a fuck.
Just sayin...
Richard Buckminster Fuller - Geodesic Domes
Isn't that what these guys Robert Curl, Harold Kroto and Richard Smalley used to make the discovery of Buckminsterfullerene? (Or Buckyballs and Buckytubes.)
This is a breakdown of your diagram correct?
Covariant also means that the properties of some "object" (like a vector) on some manifold will remain the same under certain transformations that position this object on several locations on the manifold. For example when a manifold is curved, you will always need to define some space time continuum locally on that manifold. Then you need to know that the connection between these two points on the manifold is covariant so you can be certain that for example a 0-vector in one point of this manifold will still be a 0-vector in the other point.
Or, for example, look at tensors, which are a generalization of mathematical objects like vectors, matrices,...So a tensor is basically any object with indices (like a vector or matrix or double product of two or more vectors) AND certain transformation properties. Basically, these properties are that a tensor is covariant when it is transformed. Thus, this means that for example when the elements in a tensor (like the row and colomn-elements in a matrix) are 0 in one point on the manifold, they must remain zero at some other point on the manifold.
The most famous examples are the Riemanntensor and the Riccitensor from General Relativity. The Riemanntensor can be used in order to eveluate whether a manifold is curved or not. You can use it to check that the earth is curved although in your local reference frame, everything seems flat (you can see as far as the horizon).
This tensor is calculated by using the Christoffel-symbols which are also objects with indices BUT no tensors because they are not covariant. Their structure will change as you move them along the manifold.
covariant vs contravariant
LULZ!!!
For those interested in knowing what Vectors actually are, Math Forum - Ask Dr. Math
The above figure illustrates how the contravariant and covariant representations would be plotted in terms of components on a 2D curvilinear non-orthogonal grid for a generic vector A. Note that the sum of either pair of vectors yields the same vector. Also note that the covariant basis vectors are parallel to their respective coordinate lines while the contravariant basis vectors are orthogonal to the directions of the other coordinate lines.
Isn't that what these guys Robert Curl, Harold Kroto and Richard Smalley used to make the discovery of Buckminsterfullerene? (Or Buckyballs and Buckytubes.)
This is a breakdown of your diagram correct?
Covariant also means that the properties of some "object" (like a vector) on some manifold will remain the same under certain transformations that position this object on several locations on the manifold. For example when a manifold is curved, you will always need to define some space time continuum locally on that manifold. Then you need to know that the connection between these two points on the manifold is covariant so you can be certain that for example a 0-vector in one point of this manifold will still be a 0-vector in the other point.
Or, for example, look at tensors, which are a generalization of mathematical objects like vectors, matrices,...So a tensor is basically any object with indices (like a vector or matrix or double product of two or more vectors) AND certain transformation properties. Basically, these properties are that a tensor is covariant when it is transformed. Thus, this means that for example when the elements in a tensor (like the row and colomn-elements in a matrix) are 0 in one point on the manifold, they must remain zero at some other point on the manifold.
The most famous examples are the Riemanntensor and the Riccitensor from General Relativity. The Riemanntensor can be used in order to eveluate whether a manifold is curved or not. You can use it to check that the earth is curved although in your local reference frame, everything seems flat (you can see as far as the horizon).
This tensor is calculated by using the Christoffel-symbols which are also objects with indices BUT no tensors because they are not covariant. Their structure will change as you move them along the manifold.
covariant vs contravariant
LULZ!!!
For those interested in knowing what Vectors actually are, Math Forum - Ask Dr. Math