Pensieve header: Making test matrices for JCF computations.

Matrix 1 - 3x3, 3 eigenvalues.

(R=Table[RandomInteger[{-2,2}], {3}, {3}]) // MatrixForm

Inverse[R] // MatrixForm

(Inverse[R].(({{1, 0, 0}, {0, 3, 0}, {0, 0, -2}})).R) // MatrixForm

Matrix 2 - 3x3, one Jordan block.

(R=Table[RandomInteger[{-3,3}], {3}, {3}]) // MatrixForm

Inverse[R] // MatrixForm

(Inverse[R].(({{3, 0, 0}, {1, 3, 0}, {0, 1, 3}})).R) // MatrixForm

Matrix 3 - 4x4, mixed Jordan form.

(R=Table[RandomInteger[{-2,2}], {4}, {4}]) // MatrixForm

Inverse[R] // MatrixForm

(Inverse[R].(({{1, 0, 0, 0}, {0, 2, 0, 0}, {0, 0, 2, 0}, {0, 0, 1, 2}})).R) // MatrixForm