instead of using AA, use ATA, so you get a symmetric matrix.
In each part, use the given inner product on to find ||w||, where w = (-1,3).
(a) the Euclidean inner product
(b) the weighted Euclidean inner product <u,v> = 3u1v1 + 2u2v2, where u = (u1,u2) and v = (v1,v2)
(c) the inner product generated by the matrix
Show that <u,v> = 5u1v1 - u1v2 -u2v1 + 10u2v2 is the inner product on generated by
but i couldn't get the equation above. I suppose that the above formula only hold for diagonal matrix?