Casoratian

Casoratian[{y1,y2,},n]
gives the Casoratian determinant for the sequences , , depending on n.

Casoratian[eqn,y,n]
gives the Casoratian determinant for the basis of the solutions of the linear difference equation eqn involving .

Casoratian[eqns,{y1,y2,},n]
gives the Casoratian determinant for the system of linear difference equations eqns.

DetailsDetails

  • The Casoratian determinant is defined as: Det[Table[DiscreteShift[yi,{n,j}],{i,m},{j,0,m-1}]].
  • If the sequences are linearly dependent, the Casoratian vanishes everywhere.

ExamplesExamplesopen allclose all

Basic Examples  (4)Basic Examples  (4)

These sequences are linearly independent:

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The following sequences are linearly dependent:

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Here the sequences are linearly dependent only when :

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The Casoratian for a linear equation:

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Except for a constant, the result is the same as for the explicit solution:

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Introduced in 2008
(7.0)