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Unformatted text preview: E *  {z } p R Remarks. The function T ( 1 , , p ) is linear in each argument. The functional T is independent of any basis. A contravariant vector (covector) is a contravariant tensor of rank 1. The components of the tensor T with respect to the basis i are dened by T i 1 ... i p = T ( i 1 , . . . , i p ) . Then for any covectors ( a ) = n X j = 1 ( a ) j j , where a = 1 , . . . , p , we have T ( (1) , . . . , ( p ) ) = n X j 1 ,..., j p = 1 T j 1 ... j p (1) j 1 ( p ) j p . The inverse matrix of the components of a metric tensor denes a contravariant tensor g1 of rank 2 by g1 ( , ) = n X i , j = 1 g i j i j . di geom.tex; April 12, 2006; 17:59; p. 49...
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 Spring '10
 Wong
 Geometry, Vectors, Vector Space

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