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

In summary, a Matrix Power Question is a type of question used in social science research to examine the relationship between two or more variables. It differs from other types of research questions by specifically focusing on this relationship and is often used in quantitative research. Examples of Matrix Power Questions include examining the relationship between income level and education level or age and job satisfaction. These questions are typically answered by collecting data and using statistical analysis techniques. The benefits of using Matrix Power Questions in research include the ability to test hypotheses, make predictions, and identify patterns and relationships between variables, as well as providing more precise and objective results compared to qualitative methods. They also help inform evidence-based decisions and future studies in the field.
  • #1
astonmartin
23
0

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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  • #2
What's this mysterious integer x? Is it the same as d?
 
  • #3
Yeah sorry that's supposed to be a d. I'm assuming there is a solution to this other than the negative identity matrix?
 
  • #4
Well, yes, e.g. A=[[0,1],[-1,0]] is a 2x2 matrix and A^2=-I.
 

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

What is a Matrix Power Question?

A Matrix Power Question is a type of question used in the field of social science research to examine the relationship between two or more variables. It involves measuring the strength and direction of the relationship between the variables and is often used to test hypotheses or make predictions.

How is a Matrix Power Question different from other types of research questions?

A Matrix Power Question differs from other types of research questions, such as descriptive or exploratory questions, because it specifically focuses on examining the relationship between variables. It is also often used in quantitative research, whereas other types of research questions can be used in both quantitative and qualitative studies.

What are some examples of Matrix Power Questions?

Some examples of Matrix Power Questions include: "What is the relationship between income level and education level?", "Is there a correlation between age and job satisfaction?", and "How does gender impact voting behavior?" These questions all involve examining the relationship between two variables.

How is a Matrix Power Question answered?

A Matrix Power Question is typically answered by collecting data from a sample of participants and using statistical analysis techniques to determine the strength and direction of the relationship between the variables. This can involve using tools such as correlation coefficients, regression analysis, or chi-square tests.

What are the benefits of using Matrix Power Questions in research?

Matrix Power Questions have several benefits in research, including the ability to test specific hypotheses, make predictions, and identify patterns and relationships between variables. They also allow for quantitative data analysis, which can provide more precise and objective results compared to qualitative methods. Additionally, Matrix Power Questions can help researchers make evidence-based decisions and inform future studies in the field.

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