Frédéric Brechenmacher - Centre Alexandre Koyré
Le théorème de décomposition matricielle dans le traité de Mac Duffee de 1943.
THEOREM 65. Every non derogatory matrix whose minimum function is [l(x)]h where l(x) is irreductible of degree j is similar to a matrix of the type (35) with h blocks along the diagonal.
The case where F is the complex field, or in fact any algebraically closed field, deserves special mention. In this case we can write
so that A is similar to a direct sum of matrices of the form
of hi rows and columns. This the familiar
[Mac Duffee, 1943, 114-121]