"Let [tex]m(x)[/tex] be the minimal polynomial of [tex]T:V\rightarrow V, \dim V<\infty[/tex] such that [tex]m(x)=m_1(x)m_2(x)[/tex] where [tex]gcd(m_1,m_2)=1[/tex], then there exists [tex]T[/tex]-invariant subspaces [tex]V_1, V_2[/tex] such that [tex]V=V_1\oplus V_2[/tex]."(adsbygoogle = window.adsbygoogle || []).push({});

What other names is this thoerem called? It was given to me as the "primary decomposition theorem" but it's neither in my book nor in mathworld or wikipedia.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Primary Decomposition Theorem

**Physics Forums | Science Articles, Homework Help, Discussion**