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admissibility (Definition)

Let $k$ be a field, $V$ a vector space over $k$ and $T\colon V\to V$ a linear operator. We say that a subspace $W$ of $V$ is $T$ admissible if

  1. $W$ is a $T$ - invariant subspace;
  2. If $f \in k[X]$ (See the polynomial ring definition) and $f(T)x \in W$ there is a vector $y \in W$ such that $f(T)x=f(T)y$




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Cross-references: vector, polynomial ring, invariant subspace, subspace, linear operator, vector space, field
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This is version 3 of admissibility, born on 2003-12-02, modified 2004-03-15.
Object id is 5448, canonical name is Admissibility.
Accessed 4484 times total.

Classification:
AMS MSC15A04 (Linear and multilinear algebra; matrix theory :: Linear transformations, semilinear transformations)

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