Can I Modify Order to Get X=I Matrix?

  • Context: Graduate 
  • Thread starter Thread starter somebody2
  • Start date Start date
  • Tags Tags
    Identity Matrix
Click For Summary
SUMMARY

The discussion centers on the equation ABCXC^-1A^-1B^-1=I, where the goal is to manipulate the order of operations to simplify it to X=I. Participants emphasize the importance of maintaining the equality while rearranging terms, specifically by considering the multiplication of AA^-1 and BB^-1. The consensus is that strategic premultiplication of A's inverse can facilitate the transformation to the identity matrix.

PREREQUISITES
  • Matrix algebra fundamentals
  • Understanding of matrix inverses
  • Knowledge of identity matrices
  • Familiarity with properties of matrix multiplication
NEXT STEPS
  • Study the properties of matrix inverses in detail
  • Learn about the implications of the identity matrix in linear transformations
  • Explore advanced matrix manipulation techniques
  • Research examples of rearranging matrix equations for simplification
USEFUL FOR

Mathematicians, students of linear algebra, and anyone involved in theoretical physics or engineering who requires a deeper understanding of matrix operations and simplifications.

somebody2
Messages
1
Reaction score
0
If I have ABCXC^-1A^-1B^-1=I (that is C, B, A inverse), can I modify the order so that the AA^-1, BB^-1 are multiplied to get the identity matrix so that I can get it down to X=I?
 
Last edited:
Physics news on Phys.org


It's a clue to change the equation so that it keeps the equality.
For example trying premultiplying the inverse of A...
 
Last edited:

Similar threads

Undergrad Can one find a matrix that's 'unique' to a collection of eigenvectors?
  • · Replies 33 ·
2
Replies
33
Views
2K
Undergrad How can I convince myself that I can find the inverse of this matrix?
  • · Replies 34 ·
2
Replies
34
Views
3K
Undergrad Do Metric Tensors Always Have Inverses?
  • · Replies 8 ·
Replies
8
Views
3K
Graduate How to augment a machine learning matrix?
  • · Replies 10 ·
Replies
10
Views
3K
Undergrad Solving matrix commutator equations?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Getting eigenvalues of an arbitrary matrix with programming
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Matrix rank in terms of determinant polynomial
  • · Replies 14 ·
Replies
14
Views
4K
Undergrad Determining elements of Markov matrix from a known stationary vector
  • · Replies 24 ·
Replies
24
Views
3K
Graduate What Is the Significance of the Matrix Identity Involving \( S^{-1}_{ij} \)?
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Trace of the inverse of matrix products
  • · Replies 2 ·
Replies
2
Views
2K