Finding the Set of Permutable Matrices with Algebra

  • Thread starter Thread starter esmeco
  • Start date Start date
AI Thread Summary
To determine the set of permutable matrices with a given matrix A, one must find matrices X such that AX = XA. A key point is that for a matrix to be permutable, it typically requires that all rows and columns are consistent in structure. The discussion suggests that if matrix X has the same dimensions as matrix A, there could be infinitely many exchangeable matrices. The example provided illustrates a potential structure for such matrices. Understanding the properties of matrix multiplication is crucial for identifying these permutable matrices.
esmeco
Messages
144
Reaction score
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
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:
Any thoughts on this?
 

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

A gardener collected 17 apples...
Replies
32
Views
2K
Python Partial pivoting in getting the reduced row echelon form of a matrix
Replies
2
Views
1K
I How do Tensors "work" in relation to linear algebraic objects?
Replies
7
Views
256
Bishops and permutations on chessboard
Replies
23
Views
3K
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
3K
I Is there a better way to calculate time-shifted correlation matrices?
Replies
2
Views
2K
Transformations to both sides of a matrix equation
Replies
25
Views
2K
Python Simple code example of transforming matrix into upper triangular form
Replies
3
Views
1K
How Can We Efficiently Parallelize the N-Queens Problem?
Replies
11
Views
4K

Hot Threads

Recent Insights

Back
Top