:: deftheorem Def12 defines QuadraticForm MATRIXC1:def 12 :
for x, y being FinSequence of COMPLEX
for M being Matrix of COMPLEX st len x = len M & len y = width M holds
for b₄ being Matrix of COMPLEX holds
( b₄ = QuadraticForm (x,M,y) iff ( len b₄ = len x & width b₄ = len y & ( for i, j being Nat st [i,j] in Indices M holds
b₄ * (i,j) = ((x . i) * (M * (i,j))) * ((y . j) *') ) ) );