How to find jordan form given rank?

  • Thread starter Thread starter chuy52506
  • Start date Start date
  • Tags Tags
    Form rank
chuy52506
Messages
77
Reaction score
0
How to find jordan form given rank??

Find the jordan for of A given that A is an 8x8 matrix, rank(A)=5, rank(A^2)=2, rank(A^3)=1 and rank(A^4)=0.

I know that the largest jordan block will be 4x4 and there will be only one of them since the rank(A^3)=1 but how do i find the rest??
 
Physics news on Phys.org


well how do other blocks affect the total rank?
 

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
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 Matrix rank in terms of determinant polynomial
Replies
14
Views
3K
I Uniqueness of reduced row echelon form (proof verification)
Replies
4
Views
1K
MHB Check the statements about a 4x5 matrix with rank 2.
Replies
9
Views
5K
I How can I find all possible Jordan forms?
Replies
8
Views
2K
MHB -m99.54 List possible Jordan Canonical forms for A.
Replies
11
Views
2K
MHB What Are the Possible Jordan Forms and Characteristic Polynomial of T?
Replies
1
Views
2K
MHB 25.1 find all possible Jordan Normal Forms of A
Replies
1
Views
2K
MHB 25.3 Find the Jordan Normal Form of A
Replies
7
Views
2K
A Question about the irreducible representation of a rank 2 tensor under SO(3)
Replies
5
Views
3K
I General Form of Fourth Rank Isotropic Tensor: A Scientific Inquiry
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top