ly many rows and columns, see below.නිශ්චිත භාවය[සංස්කරණය]Matrix A; definiteness; associated quadratic form QA(x,y);  set of vectors (x,y) such that QA(x,y)=1[1/4001/4]{\displaystyle {\begin{bmatrix}1/4&0\\0&1/4\end{bmatrix}}}[1/400−1/4]{\displaystyle {\begin{bmatrix}1/4&0\\0&-1/4\end{bmatrix}}}positive definiteindefinite1/4 x2 + 1/4y21/4 x2 − 1/4 y2 EllipseHyperbolaA symmetric n×n-matrix is called positive-definite (respectively negative-definite; indefinite), if for all nonzero vectors x ∈ Rn the associated quadratic form given byQ(x) = xTAxtakes only positive values (respectively only negative values; both some negative and some positive values).[25] If the quadratic form takes only non-negative (respectively only non-positive) values, the symmetric matrix is called positive-semidefinite (respectively negative-semidefinite); hence the matrix is indefinite precisely when it is n