Find Real nxn Matrices with Negative Identity Power | Matrix Power Question

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Homework Help Overview

The discussion revolves around finding real nxn matrices such that their d-th power equals the negative identity matrix, -I. Participants are exploring the implications of the matrix size and the nature of the integer involved in the problem.

Discussion Character

  • Exploratory, Conceptual clarification, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning the significance of the matrix size and the integer d, with some expressing confusion about the problem's requirements and potential solutions. There is also a consideration of specific examples, such as a known 2x2 matrix that satisfies the condition.

Discussion Status

The discussion is active, with participants clarifying terms and exploring examples. Some have provided specific matrix instances that meet the criteria, while others are still questioning the problem's parameters and the existence of other solutions.

Contextual Notes

There is ambiguity regarding the relationship between the integers x and d, as well as the implications of matrix size on the problem's solutions.

astonmartin
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Homework Statement


For what positive integers x and n is there a real nxn matrix whose d-th power is -I (negative identity matrix)


Homework Equations





The Attempt at a Solution



I don't really understand this problem, aren't there endless possibilities? Also, why does it matter what size the matrix is? :confused:
 
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What's this mysterious integer x? Is it the same as d?
 
Yeah sorry that's supposed to be a d. I'm assuming there is a solution to this other than the negative identity matrix?
 
Well, yes, e.g. A=[[0,1],[-1,0]] is a 2x2 matrix and A^2=-I.
 

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