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

catsarebad
Messages
69
Reaction score
0
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.
 
Physics news on Phys.org
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 '##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?'

I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Decomposition into irreps of compact Lie group'

When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
View full post »

Similar threads

I Can one find a matrix that's 'unique' to a collection of eigenvectors?
Replies
33
Views
652
Jordan Can. Form of Frobenius map
Replies
1
Views
4K
Finding the canonical form of a quadratic form.
Replies
3
Views
7K
I How can I convince myself that I can find the inverse of this matrix?
Replies
34
Views
3K
MHB Could someone recommend me pure math linear algebra book?
Replies
12
Views
3K
Python Partial pivoting in getting the reduced row echelon form of a matrix
Replies
2
Views
1K
Real and complex canonical forms
Replies
1
Views
3K
MHB 25.3 Find the Jordan Normal Form of A
Replies
7
Views
2K
MHB Determine vec {{x},{y},{3x+2y}} in R^3 form a vec space
Replies
11
Views
2K
MHB How Do You Find the Inverse of a Matrix Using the Adjoint Method?
Replies
15
Views
3K

Hot Threads

Recent Insights

Back
Top