Matrix Proof: A^t ~ B^t and A^-1 ~ B^-1 | Exam Time Tips

  • Thread starter Thread starter dangish
  • Start date Start date
  • Tags Tags
    Matrix Proof
Click For Summary

Homework Help Overview

The discussion revolves around proving properties of similar matrices, specifically focusing on the transpose and inverse of matrices A and B, given that A is similar to B. The subject area is linear algebra, particularly matrix theory.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about how to start the proof and whether determinants are relevant. There are discussions about the definition of matrix similarity and its implications for transposes and inverses. Questions arise regarding the relationship between similar matrices and their determinants.

Discussion Status

Participants are exploring various definitions and properties related to matrix similarity. Some have provided insights into the relationship between matrices and their transposes, while others are questioning how these concepts connect to the proof requirements. No consensus has been reached, but there are productive lines of inquiry being pursued.

Contextual Notes

There is mention of missing information regarding relevant formulas and definitions, which may impact the discussion. Participants are also considering the implications of the definitions of matrix similarity and the properties of determinants.

dangish
Messages
72
Reaction score
0
If A~B prove :
a) A^t ~ B^t (Atranspose ~ Btranspose)
b) A^-1 ~ B^-1

I don't really know where to begin.. does the determinant have anything to do with it?

Exam time let's go people!
 
Physics news on Phys.org
dangish said:
If A~B prove :
a) A^t ~ B^t (Atranspose ~ Btranspose)
b) A^-1 ~ B^-1

I don't really know where to begin.. does the determinant have anything to do with it?

Exam time let's go people!

When you deleted most of the information in the template, you deleted the section on relevant formulas and definitions. One definition that is very important here is the definition of what it means when two matrices are similar.
 
When two matricies are similar, they have the same determinant.

However, because two matricies have the same determinant does not mean they are similar.

also know that detA^t=detA

Is this good stuff?
 
The definition that I'm familiar with has to do with matrix inverses.

If A and B are similar, then B = P-1AP for some invertible matrix P.

This is the way matrix similarity is usually defined.
 
Yes I know that one, I don't see where the transpose of a matrix comes into play there
 
Since A and B are similar (given) then B = P-1AP, for some invertible P.

If two matrices are equal, what can you say about their transposes? Also, when you have the transpose of a product, what does that equal?
 

Similar threads

How to find a system of equations when the solution is given?
  • · Replies 6 ·
Replies
6
Views
2K
Direct Proof that every zero of p(T) is an eigenvalue of T
  • · Replies 24 ·
Replies
24
Views
4K
Do these two statements imply an underlying induction proof?
  • · Replies 7 ·
Replies
7
Views
1K
Avoid unpleasant integrals in solving IVP
  • · Replies 3 ·
Replies
3
Views
2K
Person i belongs to a clique iff ith diagonal entry of B^3 is positive
  • · Replies 9 ·
Replies
9
Views
2K
Transformation Matrix T in Terms of β1, β2 with Row Reduction Explained
  • · Replies 1 ·
Replies
1
Views
2K
Solving a separable matrix ODE.
  • · Replies 3 ·
Replies
3
Views
2K
Solving a first order matrix differential equation
  • · Replies 6 ·
Replies
6
Views
1K
Tricky Problem: Prove range T = null ##\phi## when null T' has dim 1
  • · Replies 8 ·
Replies
8
Views
2K
Given surjective ##T:V\to W##, find isomorphism ##T|_U## of U onto W.
  • · Replies 1 ·
Replies
1
Views
2K