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How do you find frobenius canonical form of a matrix?

chickenwin

New member
Feb 13, 2014
12
the actual problem is to show that

the given matrix is similar to companion matrix


here is the companion matrix

Companion matrix - Wikipedia, the free encyclopedia

----------------

i know that if same frobenius canonical form then similar but i don't even know how to find the frobenius form. could someone point me in the right direcion?

also if i can show that both matrix have same minimal poly then i would be done but i don't see that being easy.
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,790
the actual problem is to show that

the given matrix is similar to companion matrix


here is the companion matrix

Companion matrix - Wikipedia, the free encyclopedia

----------------

i know that if same frobenius canonical form then similar but i don't even know how to find the frobenius form. could someone point me in the right direcion?

also if i can show that both matrix have same minimal poly then i would be done but i don't see that being easy.
Hi chickenwin! Welcome to MHB! :)

Which eigenvalues and eigenvectors does your matrix have?
Can you find a companion matrix with the same eigenvalues and the same dimension of the eigenspace?