Proving Matrix Expressions: AX = XA

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Homework Help Overview

The discussion revolves around a matrix expression involving the equality AX = XA for matrices A and X in the context of linear algebra. The original poster is attempting to prove this relationship under certain conditions related to the field F.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the clarity of the original problem statement, particularly regarding the mention of "s" and its relevance to the matrix expression. There is confusion about whether the expression was correctly presented and what assumptions are being made.

Discussion Status

The discussion is currently focused on clarifying the original problem statement and addressing potential typographical errors. Participants are actively questioning the setup and the presence of specific variables in the expression.

Contextual Notes

There appears to be confusion stemming from the notation and the inclusion of the variable "s," which has not been defined in the context of the problem. This has led to uncertainty about the assumptions being made in the original poster's question.

Mathman23
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Hi

I got a question regarding a matrix expression:

Let [tex]X \in Mat_{n,n} (\mathbf{F})[/tex]. Then I'm suppose to show AX = XA for all [tex]A \in Mat_{n,n} \mathbf{(F)}[/tex] if and only if [tex]s \in \mathbf{F}[/tex]

What is the best way of going about this?

/Fred
 
Last edited:
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Did you miswrite something? What matrix expression?
 
No, It is correctly typed.

/Fred

HallsofIvy said:
Did you miswrite something? What matrix expression?
 
You did mistype something. s appears in the last three symbols and nowhere before, and the X vanishes from the question.
 
Last edited:
When I first looked at it there was no matrix expression! May have been the server was slow in loading the LATEX. However, as Matt said, "if and only if [tex]s \in \mathbf{F}[/tex] makes no sense as there is no "s" in the hypothesis.
 

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