/sci/ - Science & Math

>>10077903

This is the one that has me stumped: 2.21.c.

I'm not sure how you'd arrive at the generalization
(x1y2 - x2y1)^2 => sigma( (xiyj - xjyi)^2) for i<j
to start with.

I understand the two 'note that' series.

The calculation of the difference, no clue again.
From i different from j, to 2 times some sum running over i<j.
Is the factor of two there because i<j excludes half the "space"
of running over i different from j? (The portion where j<i?).

Where did the xj^2*yi^2 term suddenly pop up from?