Recent content by volcano5683

Could anybody help me to check my program? I still really don't understand why program read the wrong input array. Thank you very much!

Thanks to your help, The author define that ##(\operatorname{tr} \mathbf{A})\mathbf{u} \cdot(\mathbf{v}\times\mathbf{w}) = (\mathbf{Au})\cdot(\mathbf{v}\times\mathbf{w}) +\cdots## for all ##\mathbf{u},\mathbf{v},\mathbf{w}\in\mathbb R^3##. And he proved the TrA = Aii using the properties...

I think the proof can be made for general equation when we use definition TrA = Aii. The author prove the equation using 3 basic vector only. Could the author's definition be true for any tensor A, vetors a, b, and c? That is what I want to know. Thanks

I understand trA = Aii. But I want to proof this definition. Because the definition from most other book is: trA = Aii

This program can run but I get wrong result. When I "write" the input array on the screen, I see the program read the wrong array that is different with input file. It read also the first line, and blank space as element of array.

Hi Hunt mat, You can find that identity on the book "Introduction to Continuum mechanics for engineers, revised edition 2007 by Ray M.Bowen". The equatuion is placed on page 266, Appendix A, equation No. A.5.37, but without proof. That why I can not understand.

To Fredrik, Yeah, the Aa is supposed to be interpreted as the dot product of an n x n and nx 1 but that is special case. I would like to make a proof in general case then indices of tenor A and a should be independent. Thanks

Thanks to Hunt mat, and Fredrik I think for any tensor A and vector a, b, c. We should write in their component as: \mathbf{A}\mathbf{a}=A_{mn}a_{i}\quad (\mathbf{b}\times\mathbf{c})_{i}=\varepsilon_{ijk}b_{j}c_{k} And so: \mathbf{A}\mathbf{a}\cdot...

Hi Hunt mat Here I just type using Latex. Could you check it for me? Aa.(b x c) = Amn(em \otimes en)aiei . (bjej \times ckek) = Amn(en.ei)aiem) . \epsilonijkbjckei = Amiem.ei\epsilonijkaibjck = Amm\epsilonijkaibjck Thanks

Hi every one. I had try to make a simple program but it doesn't work because i am an amateur The program as following: PROGRAM: Sum_row_n_col ! ! PURPOSE: Read the 2-rank array from input disk file and calculate sums of all of the data in each row and each column in the array. ...

Thanks to Hunt mat Could I derive Aa.(b x c) as following: Aa.(b x c) = Amn(em \otimes en) aiei.(bjej x ckek) = Amnδniaiem.(bjej x ckek) = Amiaiem.εijkbjckei = Amiδmiεijkaibjck = Ammεijkaibjck Is it similar to your...

Homework Statement Could someone guide me to proof following equation. For any A is a tensor; a, b, c are vectors. Proof that: Tr (A) a.(b x c) = Aa.(b x c) + a.(Ab x c) + a. (b x Ac) with (.) is dot product, and (x) is cross product of vector Homework Equations The...