The Theory of General Relativity And Gravitation Based On a Course of Lectures
The Theory of General Relativity And Gravitation Based On a Course of Lectures
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In our eReader you can find the full English version of the book. Read The Theory of General Relativity And Gravitation Based On a Course of Lectures Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Theory of General Relativity And Gravitation Based On a Course of Lectures
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To quickly assess the difficulty of the text, read a short excerpt:
In fact, by (24) and (25), dx! d But the Xi, # 2, etc. , being mutually independent, the bracketed expression (to be summed over all i) vanishes for all K=F\ and equajs 1 for K = X. Whence, A' l B t ' = A K B K = A l B t, (26) which was to be proved.
Any invariant, S= S f, is also called a scalar or a tensor of rank zero, since, in a manifold of n dimensions, it has n com- ponents, i. E. But one component. Similarly, a vector or tensor of rank one, has n l = n, in our case four, components. The... question whether a scalar is a contravariant or a covariant tensor is idle. For it transforms into itself.
Vice versa, it can easily be proved that if B K be four (generally, n) magnitudes such that A* B K is invariant for any contravariant A", then B K is a covariant vector. And SECOND RAN^ TENSORS 43 the same thing is true if 'covariant' and ' contra variant ' be exchanged with one another.
The product of a vector by a scalar is, obviously, again a vector of the same kind, and any number of vectors of the same kind multiplied by scalars and added together give again a vector of the same kind.
What to read after The Theory of General Relativity And Gravitation Based On a Course of Lectures?
You can find similar books in the "Read Also" column, or choose other free books by Ludwik Silberstein to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
In fact, by (24) and (25), dx! d But the Xi, # 2, etc. , being mutually independent, the bracketed expression (to be summed over all i) vanishes for all K=F\ and equajs 1 for K = X. Whence, A' l B t ' = A K B K = A l B t, (26) which was to be proved.
Any invariant, S= S f, is also called a scalar or a tensor of rank zero, since, in a manifold of n dimensions, it has n com- ponents, i. E. But one component. Similarly, a vector or tensor of rank one, has n l = n, in our case four, components. The... question whether a scalar is a contravariant or a covariant tensor is idle. For it transforms into itself.
Vice versa, it can easily be proved that if B K be four (generally, n) magnitudes such that A* B K is invariant for any contravariant A", then B K is a covariant vector. And SECOND RAN^ TENSORS 43 the same thing is true if 'covariant' and ' contra variant ' be exchanged with one another.
The product of a vector by a scalar is, obviously, again a vector of the same kind, and any number of vectors of the same kind multiplied by scalars and added together give again a vector of the same kind.
What to read after The Theory of General Relativity And Gravitation Based On a Course of Lectures?
You can find similar books in the "Read Also" column, or choose other free books by Ludwik Silberstein to read onlineMoreLess
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