What are all the matrices that commute wit a matrix of ones?

Click For Summary
SUMMARY

The discussion focuses on identifying the characteristics of matrices that commute with a matrix of ones. It is established that for a matrix to commute with a matrix of ones, the sum of each row and each column must be equal. This conclusion is derived from analyzing a 2x2 matrix and generalizing the findings. The participants confirm the validity of this property through dialogue, emphasizing the importance of understanding the definition of "commute" in matrix operations.

PREREQUISITES
  • Understanding of matrix operations and properties
  • Familiarity with the concept of matrix commutativity
  • Basic knowledge of linear algebra
  • Ability to work with 2x2 matrices
NEXT STEPS
  • Research the properties of commutative matrices in linear algebra
  • Explore the implications of commuting matrices in higher dimensions
  • Study the role of eigenvalues and eigenvectors in matrix commutativity
  • Learn about the applications of commuting matrices in various mathematical fields
USEFUL FOR

Students studying linear algebra, educators teaching matrix theory, and anyone interested in the mathematical properties of matrices and their applications.

Jamin2112
Messages
973
Reaction score
12

Homework Statement



What are the characteristics of a matrix that commutes with a matrix of ones?

Homework Equations



None.

The Attempt at a Solution



I'm helping a buddy with his homework and I can't figure out this problem.
 
Physics news on Phys.org
Try working it out explicitly for a 2x2 matrix (it's easy) and see if you can generalize from there.
 
Relevant equations None.
What about the definition of "commute"?
 
Figured out the answer, I think. The sum of every row and column is the same.
 
Jamin2112 said:
Figured out the answer, I think. The sum of every row and column is the same.

Sounds right, can you prove it?
 
Dick said:
Sounds right, can you prove it?

Yes, but the problem doesn't ask me to
 
Jamin2112 said:
Yes, but the problem doesn't ask me to

Fair enough.
 

Similar threads

Understanding Commutativity and Eigenvalues in the Product of Hermitian Matrices
  • · Replies 9 ·
Replies
9
Views
2K
Proof regarding determinant of block matrices
  • · Replies 5 ·
Replies
5
Views
5K
Does there exist a 2x2 non-singular matrix with only one 1d eigenspace?
  • · Replies 2 ·
Replies
2
Views
2K
Normal matrix as sum of self adjoint and commuting matrices
  • · Replies 5 ·
Replies
5
Views
3K
Proving statements about matrices | Linear Algebra
  • · Replies 25 ·
Replies
25
Views
3K
Commutative 2x2 Matrices: Finding Solutions for AB = BA
  • · Replies 6 ·
Replies
6
Views
2K
Find the sampling matrix and sampling structure for R, G and B components
  • · Replies 2 ·
Replies
2
Views
2K
What does a row matrix represent geometrically?
  • · Replies 8 ·
Replies
8
Views
1K
If a matrix commutes with all nxn matrices, then A must be scalar.
  • · Replies 9 ·
Replies
9
Views
13K
Hermitian Matrix and Commutation relations
  • · Replies 2 ·
Replies
2
Views
3K