I have the following questions on my biomechanics homework (we're finally getting to multidimensional spaces). However, we haven't gone over it yet and won't have class again until after it's due. I've been able to do some of it, but have no idea on the rest.
Comment on the validity of each of the following expressions in index notation (12 points):
(a) $a_i b_j = c_i (d_k - f_k)$ - I said this was invalid as the LHS is defined in terms of the indices (i,j) but the RHS is defined in terms of (i,k)
(b) $a_m b_s = c_s (d_s - f_s)$ - I said this is valid, LHS and RHS indicies are equal.
(c) $a_i = b_j c_i b_i$ - Invalid, as i is repeated on the RHS, the RHS is only in terms of j and i=!j.
(d) $x_j x_j = r^2$ - ???
(e) $a_i = 3$ - Valid. This is an array with the ith position being equal to 3.
(f) $A_{kk} = 7$ - ???, but I'd guess valid. A multidimensional array with the k,kth position being equal to 7.
I found this How to decide whether and equation in index notation is valid), but it doesn't cover all of my questions. Any help is greatly appreciated!
