ABSTRACT
Let https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756478/4cadc9cc-32ae-4840-8f83-07e1ed499955/content/pg2_12.tif"/> be a vector space over a field Φ with a non-degenerate symmetric bilinear form (x,y). We form the vector space https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756478/4cadc9cc-32ae-4840-8f83-07e1ed499955/content/pg2_13.tif"/> and define a bilinear multiplication in https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756478/4cadc9cc-32ae-4840-8f83-07e1ed499955/content/pg2_14.tif"/> such that l⋅a = a = a⋅l for every a and x⋅y = (x,y)l for x, y in https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756478/4cadc9cc-32ae-4840-8f83-07e1ed499955/content/pg2_15.tif"/> . Thus we have for α,β in Φ and x,y in https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756478/4cadc9cc-32ae-4840-8f83-07e1ed499955/content/pg2_16.tif"/> : () ( α 1 + x ) ( β 1 + y ) = ( αβ + ( x , y ) ) 1 + αy + βx https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203756478/4cadc9cc-32ae-4840-8f83-07e1ed499955/content/eq12.tif"/>
