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Composition Theorem

The composition theorem states that, given a quadratic form

Q(x,y)=x^2+y^2,
(1)
Q(x,y)Q(x^',y^')=Q(xx^'-yy^',x^'y+xy^'),
(2)

since

(x^2+y^2)(x^('2)+y^('2))=(xx^'-yy^')^2+(xy^'+x^'y)^2
(3)
=x^2x^('2)+y^2y^('2)+x^('2)y^2+x^2y^('2).
(4)

See also

Genus Theorem, Quadratic Form

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Cite this as:

Weisstein, Eric W. "Composition Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CompositionTheorem.html

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