Finding the Set of Permutable Matrices with Algebra

  • Thread starter esmeco
  • Start date
In summary, The set of permutable matrices with a square matrix A can be determined by finding all matrices with the same number of rows and columns as A, where all rows and columns are the same. There may be an infinite number of matrices that are exchangeable with A under these conditions.
  • #1
esmeco
144
0
I have this question as homework from my Algebra class:
A square matrix X is called exchangeable with A if AX=XA.Determine the set of permutable matrices with
matrix.jpg
.

My question is,how do I find that set?I know that a matrix to be permutable all rows and columns must be the same and that a square matrix is composed by the same number of rows and columns.
Thanks in advance for the help!:wink:
 
Physics news on Phys.org
  • #2
An example of a matrix that could be exchangeable with A could be X=2 3 ?
4 5

I think there would be an infinite number of matrices exchangeable with the matrix A if the matrix has the same number of rows and columns as matrix A.
 
Last edited:
  • #3
Any thoughts on this?
 

FAQ: Finding the Set of Permutable Matrices with Algebra

What is the definition of permutability in matrices?

Permutability in matrices refers to the ability to rearrange the rows and columns of a matrix without changing its overall structure or properties. This means that the resulting matrix is equivalent to the original one, but with its elements in a different order.

How can I determine if a matrix is permutable?

A matrix is permutable if its rows and columns can be rearranged to form a diagonal matrix. This can be done by using elementary row and column operations, such as swapping rows or columns, multiplying a row or column by a nonzero number, or adding a multiple of one row or column to another.

Can all matrices be permuted?

No, not all matrices can be permuted. Matrices that are not square, or have complex elements, cannot be permuted. Additionally, matrices with certain properties, such as being symmetric or orthogonal, cannot be permuted while maintaining those properties.

What is the importance of finding the set of permutable matrices with algebra?

Finding the set of permutable matrices with algebra is important in many areas of mathematics, such as linear algebra and group theory. It allows for easier manipulation and analysis of matrices, as well as providing a deeper understanding of their properties and relationships with other mathematical concepts.

Are there any applications of permutability in matrices?

Yes, permutability in matrices has many practical applications, such as in computer graphics, data compression, and cryptography. It is also used in solving systems of equations and determining the eigenvalues and eigenvectors of a matrix.

Similar threads

A gardener collected 17 apples...
Replies
32
Views
1K
Bishops and permutations on chessboard
Replies
23
Views
2K
B Is it invalid to redefine the sgn function in this way in a proof?
Replies
15
Views
4K
Identifying matrices as REF, RREF, or neither
Replies
1
Views
2K
I Is there a better way to calculate time-shifted correlation matrices?
Replies
2
Views
1K
Transformations to both sides of a matrix equation
Replies
25
Views
2K
How Can We Efficiently Parallelize the N-Queens Problem?
Replies
11
Views
2K
B Combinatorics and Magic squares
Replies
2
Views
2K
Algorithm to matrix product MSR format
Replies
3
Views
1K
Find Permutability of Matrices: Algebra Homework Help
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top