Euler four-square identity

The Euler four-square identity simply states that

(x12+x22+x32+x42)(y12+y22+y32+y42)= (x1y1+x2y2+x3y3+x4y4)2+(x1y2-x2y1+x3y4-x4y3)2 +(x1y3-x3y1+x4y2-x2y4)2+(x1y4-x4y1+x2y3-x3y2)2

It may be derived from the property of quaternions that the norm of the product is equal to the product of the norms.

Title Euler four-square identity
Canonical name EulerFoursquareIdentity
Date of creation 2013-03-22 12:35:20
Last modified on 2013-03-22 12:35:20
Owner vitriol (148)
Last modified by vitriol (148)
Numerical id 6
Author vitriol (148)
Entry type Theorem
Classification msc 11N32
Related topic Quaternions
Related topic MultiplicativityOfSumsOfSquares
Related topic LagrangesFourSquareTheorem
Related topic SumsOfTwoSquares