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By Zlatko Jankocic

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Additional resources for A Contribution to the Vector and Tensor Analysis: Course Held at the Department for Mechanics of Deformable Bodies September – October 1969

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In spite of the fact that we developed the described scheme for finite-dimensional vector spaces X(n) it can usefully be applied in a discussion of more general cases, i. e. in infinite-dimensional spaces X (oo) and X (C) He re we do not give a full and rigorous report but indicate Vector and Tensor Algebra 42 some plausible changes tobe made with some illustrations for application. First, we have to interpret the summation over double indices as sums with an infinite number of terms for n =- oo and as integrals over double in- dices for the continuum.

5 1 ' (5. l2a) or explicitly written {for brevity we ornit je' _e' ( f T'- pr) e' l e'_ e'_ h t e p r (5. l2b) Hence the transformation law Vector and Tensor Algebra 38 for the tensor components follows at once. ) in the product ()(, , i. e. they are >X, space belang to the same of the same dimension X n >x, X< ) x< and their valences mutually inter- act. Then, we could omit and abbreviate the notation as tX. illustrated by the example of the tensor (compare with (5. 3)} > > r< < < ie ke ( i *Te X= in the product space pr) ~e e e P 5o' >x ® >X (5.

6) have tobe inverse operators one to the other. Thus, they satisfy the relations t>-r;_ X =r: e. = . 5. e . T)< xr ~ " L J J' Y> ~L j>~Y (. >~i 6 (X -Y) = xe t y = ey ' - (6. 8a) E X>

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