Content deleted Content added
m add link |
|||
Line 417:
By the [[extreme value theorem]], this continuous function attains a maximum at some {{tmath|\mathbf u}} when restricted to the unit sphere <math>\{\|\mathbf x\| = 1\}.</math> By the [[Lagrange multipliers]] theorem, {{tmath|\mathbf u}} necessarily satisfies
<math display=block>\nabla \mathbf{u}^\operatorname{T} \mathbf{M} \mathbf{u} - \lambda \cdot \nabla \mathbf{u}^\operatorname{T} \mathbf{u} =
for some real number {{tmath|\lambda.}} The nabla symbol, {{tmath|\nabla}}, is the [[del]] operator (differentiation with respect to {{nobr|{{tmath|\mathbf x}}).}} Using the symmetry of {{tmath|\mathbf M}} we obtain
| |||