Primary Decomposition theory

Dears,

Could you please help me in proving the following:

" Let be a linear opearator on finite dimensional spsce , let be a minimal polynomial for , and let be the primary decomposition for , i.e., is the null space of

. Let be any subspace of which is invarient under . Prove that

"

With Best Wishes

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Re: Primary Decomposition theory

The canonical decomposition of a vector space with respect to a linear transformation T can be found in any good linear algebra book. The solution to your problem is really just understanding this decomposition:

Attachment 27899