Register to reply

Block matrix transformation of specific form

by SNicolas
Tags: block, form, matrix, specific, transformation
Share this thread:
SNicolas
#1
Feb20-13, 04:38 AM
P: 2
Hi everyone,

I am trying to solve the following problem. Is there exist a transformation matrix T, different then the block diagonal, with all blocks the same, such that the form of the matrix A=[A1 A2 ; I 0], is preserved? All blocks of A are in R^{nxn}, I is identity and 0 is zero matrix. In other words, is there exist matrix T (again, not block diagonal with all blocks the same) such that T^{-1}*A*T=B, where B=[B1 B2 ; I 0]?
By intuition, such matrix T does not exist, but I do not know how this can be shown.
If anyone has an idea about this please help. Thank you in advance.

Nicolas
Phys.Org News Partner Science news on Phys.org
What lit up the universe?
Sheepdogs use just two simple rules to round up large herds of sheep
Animals first flex their muscles
mfb
#2
Feb20-13, 08:17 AM
Mentor
P: 11,869
So T should be like [t t; t t]?
For the lower blocks of B, this would give the equations 1*t + 0*t = 1 and 1*t + 0*t = 0 => contradiction
SNicolas
#3
Feb20-13, 08:31 AM
P: 2
Thanks for your reply.

Since I am looking for the existence of T, in general it could be
T=[T11 T12 ; T21 T22]. I know that T=[T 0; 0 T] holds, but I want to show that this is the only case. For example T=[T11 0 ; 0 T22] cannot hold, neither the example that you proposed.

mfb
#4
Feb20-13, 11:23 AM
Mentor
P: 11,869
Block matrix transformation of specific form

Ok, I was not sure what "with all blocks the same" means.
Anyway, [t t; t t] matrix would not have an inverse matrix.


Register to reply

Related Discussions
How to put a matrix in its block diagonal form (Mathematica) Math & Science Software 2
Linear Transformation to Block-wise Stack Matrix Linear & Abstract Algebra 11
Matrix in Block Form Calculus & Beyond Homework 5
Block diagonal form and diagonal matrix General Math 0
Help finding a transition matrix between the Jordan form and a general form Calculus & Beyond Homework 5