Bilineaarvorm
Olgu Vn n-mõõtmeline vektorruum. R {\displaystyle \mathbb {R} } olgu reaalarvude hulk. Funktsiooni ψ: Vn x Vn → R {\displaystyle \mathbb {R} } nimetatakse bilineaarvormiks, kui iga x → {\displaystyle {\vec {x}}} , y → {\displaystyle {\vec {y}}} , z → {\displaystyle {\vec {z}}} ∈ Vn korral ning iga a,b ∈ R {\displaystyle \mathbb {R} } korral kehtib: ψ(a* x → {\displaystyle {\vec {x}}} + b* y → {\displaystyle {\vec {y}}} , z → {\displaystyle {\vec {z}}} ) = a*ψ( x → {\displaystyle {\vec {x}}} , z → {\displaystyle {\vec {z}}} ) + b*ψ( y → {\displaystyle {\vec {y}}} , z → {\displaystyle {\vec {z}}} ) ψ( x → {\displaystyle {\vec {x}}} , a* y → {\displaystyle {\vec {y}}} + b* z → {\displaystyle {\vec {z}}} ) = a*ψ( x → {\displaystyle {\vec {x}}} , y → {\displaystyle {\vec {y}}} ) + b*ψ( x → {\displaystyle {\vec {x}}} , z → {\displaystyle {\vec {z}}} ) Bilineaarvormide hulka tähistatakse: Lin(VnxVn, R {\displaystyle \mathbb {R} } )