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
Quioque, New York

... are 65 years of age or older. The median age is 39 years. For every 100 females there are 113.3 males. For every 100 females age 18 and over, there are 108.7 males. The ...

 
 
 
This page was created in 22.3 ms