Expected Value and covariance of matrix

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Discussion Overview

The discussion revolves around the calculation of the expected value and covariance of a 2x1 matrix (vector). Participants explore the definitions and implications of these statistical concepts in the context of matrix operations, particularly focusing on the mean and covariance formulas.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about finding the expected value E[A] of a 2x1 matrix A and seeks clarification on the resultant dimensions.
  • Another participant suggests that the definition of the "mean of a matrix" is crucial, noting that if the elements of the matrix follow a Gaussian distribution centered around 0, the average vector would have all entries as 0, but this is contingent on the chosen distribution and its parameters.
  • A link to an external resource is provided by a participant as a starting point for understanding covariance and related concepts.
  • A follow-up question is posed regarding the necessity of having a data set to compute covariance for a 2x1 matrix, indicating uncertainty about the requirements for such calculations.

Areas of Agreement / Disagreement

Participants express differing views on the definition of the mean of a matrix and the conditions under which covariance can be calculated, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

There are limitations in the discussion regarding the assumptions about the distributions of matrix elements and the requirement of data sets for covariance calculations, which remain unclear.

tommyhakinen
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I have a 2x1 matrix A. I would like to find out E[A] which is the mean of the matrix. How do I do this? what is the dimension of the resultant matrix? using this E[A], I am going to find the covariance of matrix A by this formula

cov(A) = E[(A - E[A])(A - E[A])^{T})

could someone please enlighten me? thank you in advance.
 
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tommyhakinen said:
I have a 2x1 matrix A. I would like to find out E[A] which is the mean of the matrix. How do I do this? what is the dimension of the resultant matrix? using this E[A], I am going to find the covariance of matrix A by this formula

cov(A) = E[(A - E[A])(A - E[A])^{T})

could someone please enlighten me? thank you in advance.


It depends on what you mean by the "mean of a matrix". I assume you are trying to find out what the elements of the matrix should be. Well if each element has a Gaussian distribution centered around 0, then the "average" vector should have all of its entries as 0. But this depends on your choice of distribution, mean for the element entries, and standard deviation.

Try to better define what you are saying
 
brydustin said:
I think you had better look at this:
http://www.itl.nist.gov/div898/handbook/pmc/section5/pmc541.htm
to get started.

Thanks for the reply. but if my matrix A is a 2x1 vector which only has two elements, is it possible to find the covariance or i have to have the set of data in order to get the covariance?
 

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