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seen Oct 16 at 15:05

quadratic linear form XFX with matrix

F:  1   1
    1   1

in canonical base can be expressed as X' F' X'

X'  1   0   X'   
    0   0

where X'=A-1X, F'=AFA and A is transition matrix. Canonical base vectors are [1,0] and [-1,1]. Thus this is correct that (a+b)^2 = a^2 + b^2 + 2ab