2] is the discriminant of the eigenvalue equation for the velocity gradient.
2](T) depends on the sign of the discriminant of the eigenvalue equation for [nabla][v.
By applying the variational operation to recast Equation (2), the spatial basis can be obtained from the following eigenvalue equation
According to Proposition 2, the problem of solving the constrained optimization function is transformed to the problem of solving eigenvalue equation
shown in (19).
The calculations involved in trying to directly solve an eigenvalue equation
for an actual system of say, one million equations, would be formidable.
The solutions of the eigenvalue equation
Cx = x[lambda] imply the given quadratic equation and its solutions.
The eigenvalue equations
are then reduced to a finite linear system: