Prof, the 50 solved problems have been very helpful. They are well simplified. Only I didn’t understand how you arrived at the answer in question 28. Still trying to understand how gjkδjiφ,k+xi,kφ,j+xiφ,jk leads to the answer.

First, note that when we are dealing with Orthonormal Bases (ONB) such as the Cartesian, the raised and lower indices coincide. Furthermore, all the metric tensors (with raised or lowered indices) become Kronecker deltas.
I will rearrange that solution next time I edit the notes. See me if you still find it difficult.

Sir i believe a condition of some sort would exist for
UΦV=(VΦU)T.
Could you determine the vector U. Sir.
The symbol i used would represent outer product.
T -transpose.

Prof, the 50 solved problems have been very helpful. They are well simplified. Only I didn’t understand how you arrived at the answer in question 28. Still trying to understand how gjkδjiφ,k+xi,kφ,j+xiφ,jk leads to the answer.

First, note that when we are dealing with Orthonormal Bases (ONB) such as the Cartesian, the raised and lower indices coincide. Furthermore, all the metric tensors (with raised or lowered indices) become Kronecker deltas.

I will rearrange that solution next time I edit the notes. See me if you still find it difficult.

Sir i believe a condition of some sort would exist for

UΦV=(VΦU)T.

Could you determine the vector U. Sir.

The symbol i used would represent outer product.

T -transpose.

True for every vector U