By Zlatko Jankocic
Read or Download A Contribution to the Vector and Tensor Analysis: Course Held at the Department for Mechanics of Deformable Bodies September – October 1969 PDF
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Extra info for A Contribution to the Vector and Tensor Analysis: Course Held at the Department for Mechanics of Deformable Bodies September – October 1969
6) between the spaces and X (oa) X (C) would find its deeper sense in the light of the well- known theorem space f-1 sp&ce H [ 4] : Any complex (real) separable Hilbert is isometric and isomorphic to the complex (real) and, consequently, all complex (real) separable spaces are isometric and isomorphic one to another. We arenot going here to dis- cuss many possible applications of the described approach for the infinite dimensional case, but we only mention that this approach could be useful in many fields, e.
E. ~ (6. lOa) 45 Chap. VI - Remarks ' and the analogous relations for the ket vector forms. W e point out that the scalar product is invariant . > If case b) X> b (6. lOb) is taken into consid- eration, from the relations (6. 6) itfollows ~. (X) • ~ The functions (6. 11) represent an infinite orthorrormal ~~(X) complete set of functions as shown frorn (6. 8a} when written in the conventional rnanner (6. f. o. ' r = d (X- (6. Sb} Y) l is the inte rval of the variable X 46 Vector and Tensor Algebra In case b) the relations (6.
The number r i s called the rank of the tensor. _e. ( 2 )(. t ( 3) e " t e P C4) er ( 5) (5. >-)((1) = 1, 2, . . , n1 ) etc. , the product space being 1> 2> x< 3 <4
x c1) >x c2l x<<3) x< C4> x4':. es) (5. 4a) with the basis vectors ie (1) ke (2) e e (3) eP (4) e,. (5. 4b) (5) linearly dependent on the basis vectors of the factor spaces. The type of the tensor (5. 3) is indicated by (5. 4c) Jf= and the number of its components is equal to Similarly to the vectors (Ch. I), the tensors in the same product space X tracted and multiplied by the scalars ( e can be added, sub- K ).
A Contribution to the Vector and Tensor Analysis: Course Held at the Department for Mechanics of Deformable Bodies September – October 1969 by Zlatko Jankocic