Important: The linalg package has been deprecated. Use the superseding command VectorCalculus[Wronskian], instead.

- For information on migrating linalg code to the new packages, see examples/LinearAlgebraMigration.

The procedure wronskian(f, v) computes the wronskian matrix of f with respect to v. The (i,j)th entry of the matrix result is $\frac{{\partial }^{i-1}}{\partial v^{i-1}}{f}_j$. The wronskian determinant is the determinant of the wronskian matrix.

The command with(linalg,wronskian) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{linalg}\right)\:$

$A≔\mathrm{vector}\left(\left[\exp \left(x\right)\,\cosh \left(x\right)\,\sinh \left(x\right)\right]\right)$

$A≔\left[\begin{array}{ccc}{\ⅇ}^x& \cosh \left(x\right)& \sinh \left(x\right)\end{array}\right]$

$\mathrm{Wr}≔\mathrm{wronskian}\left(A\,x\right)$

$\mathrm{Wr}≔\left[\begin{array}{ccc}{\ⅇ}^x& \cosh \left(x\right)& \sinh \left(x\right)\\ {\ⅇ}^x& \sinh \left(x\right)& \cosh \left(x\right)\\ {\ⅇ}^x& \cosh \left(x\right)& \sinh \left(x\right)\end{array}\right]$

$\det \left(\mathrm{Wr}\right)$

$0$