MHB How do you find frobenius canonical form of a matrix?

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the actual problem is to show that

the given matrix is similar to companion matrix
ijn53.jpg


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.
 
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chickenwin said:
the actual problem is to show that

the given matrix is similar to companion matrix
ijn53.jpg


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?
 
Thread 'Derivation of equations of stress tensor transformation'

Thread 'Derivation of equations of stress tensor transformation'

Hello ! I derived equations of stress tensor 2D transformation. Some details: I have plane ABCD in two cases (see top on the pic) and I know tensor components for case 1 only. Only plane ABCD rotate in two cases (top of the picture) but not coordinate system. Coordinate system rotates only on the bottom of picture. I want to obtain expression that connects tensor for case 1 and tensor for case 2. My attempt: Are these equations correct? Is there more easier expression for stress tensor...
View full post »

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