Could anyone give me some feedback, if I'm doing Ex. 1.1b from Szabo/Ostlund correctly?

The exercise is:

if O\vec{a} = \vec{b},

then show that b_i = \sum_j O_{i,j} a_j

Also, from the book we know, that \vec{a} = \sum_i \vec{e}_i*a_i.

Therefore:

O*\sum_i \vec{e}_i*a_i = \sum_j \vec{e}_j*bj

\vec{e}_j*O*\sum_i \vec{e}_i*a_i = \vec{e}_i*\sum_j \vec{e}_j*b_j

O*\sum_i \vec{e}_i*\vec{e}_j*a_i = b_i

O*\sum_i a_i = b_i

And now, we choose an arbitrary 'j' column. So,

\sum_i O_{i,j}*a_i = b_i.

Does this make sense?

Thanks for any feedback.

« Last edit by agunina on Wed Nov 30, 2016 6:18 am. »