Proving Similarity of Matrices with Same Polynomials

  • Thread starter Thread starter hiddenleaf
  • Start date Start date
  • Tags Tags
    Matrices
hiddenleaf
Messages
1
Reaction score
0

Homework Statement


Let A and B be 3x3 matrices over a field F. Prove that A and B are similar if and only if they have the same characteristic polynomial and the same minimal polynomial.


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
start with the equation relating similar matricies
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Similar threads

Confusion about definition of a splitting field
Replies
1
Views
1K
How to check if a polynomial is irreducible over the rationals
Replies
18
Views
4K
Are Similar Matrices' Eigenvalues the Same? Solving for Symmetric Matrices
Replies
9
Views
1K
Irreducibility of a Polynomial
Replies
12
Views
2K
Solving for Inverse of a Complex Matrix with Cayley-Hamilton Theorem
Replies
9
Views
2K
Given a polynomial p, prove A^2-B^2 = p(1)p(-1)
Replies
2
Views
1K
Proving Similarity of Inverse Matrices
Replies
15
Views
22K
Finding the minimal polynomial over Q
Replies
27
Views
6K
Orthogonal and Diagonal Matrices
Replies
11
Views
3K
Given specific v, dimension of subspace of L(V, W) where Tv=0?
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top