In coordinates ''x''₁, ''x''₂, ..., ''x''_''D''+1, the general quadric is thus defined by the algebraic equation
:

which may be compactly written in vector and matrix notation as:

where 1=''x'' = (''x''₁, ''x''₂, ..., ''x''_''D''+1) is a row vector, x^T is the transpose of x (a column vector),