Encyclopedia > Minimal polynomial

  Article Content

Minimal polynomial

The minimal polynomial of an n-by-n matrix A over a field F is the monic[?] polynomial p(x) over F such that p(A)=0.

The following three statements are equivalent:

  1. λ∈F is a root of p(x),
  2. λ is a root of the characteristic polynomial of A,
  3. λ is an eigenvalue of A.

The multiplicity of a root λ of p(x) is the geometrical multiplicity of &lambda and is the size of the largest Jordan block[?] corresponding to &lambda.

This is still a stub.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Explorer

... the source of the Nile, discovered Lake Tanganyika Richard E. Byrd, (1888-1957), explorer C John Cabot (Giovanni Caboto) - Italian navigator in English service, ...

 
 
 
This page was created in 22.7 ms