If a matrix group is reducible, then it is completely reducible, i.e., if the matrix group is equivalent to the matrix group in which every matrix has the reduced form
![[D_i^((1)) X_i; 0 D_i^((2))],](/images/equations/MaschkesTheorem/NumberedEquation1.svg) |
then it is equivalent to the matrix group obtained by putting 
.
Maschke's Theorem
See also
Matrix GroupExplore with Wolfram|Alpha
References
Lomont, J. S. Applications of Finite Groups. New York: Dover, p. 49, 1987.Referenced on Wolfram|Alpha
Maschke's TheoremCite this as:
Weisstein, Eric W. "Maschke's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MaschkesTheorem.html