Calculating the Mean Value of Vector n_i*n_j in 3D Space - Help and Explanation

In summary, the vector mean value is the average of a set of vectors, taking into account both direction and magnitude. It is used in data analysis to summarize trends and compare data sets. In higher dimensions, it is calculated by finding the average of coordinates in each dimension. It can be negative if the majority of vectors have negative values.
  • #1
begyu85
5
0
vector mean value - help!

Homework Statement



Let n = (n_1, n_2, n_3) be a random unit vector in Descartes coordinates in the 3-dimensional space.

What is the mean value (or expectation value) of n_i*n_j, where i,j = 1,2,3.

Or shortly: < n_i*n_j > = ?
 
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  • #2
Welcome To Pf.

Pls Show Some Work.
 
  • #3
i think, this mean value is a tensor of 3x3
 
  • #4
Why do you think that? You still haven't shown any work.
 

FAQ: Calculating the Mean Value of Vector n_i*n_j in 3D Space - Help and Explanation

What is the definition of vector mean value?

The vector mean value is a mathematical concept that represents the average of a set of vectors. It is calculated by summing all the vectors in the set and then dividing the sum by the number of vectors in the set.

How is vector mean value different from scalar mean value?

Vector mean value takes into account both the direction and magnitude of the vectors in the set, while scalar mean value only considers the numerical values. This means that vector mean value is a more comprehensive measure than scalar mean value.

What is the significance of vector mean value in data analysis?

In data analysis, vector mean value is used to summarize the overall trend or direction of a set of data points. It can also be used to compare different sets of data and identify any patterns or differences between them.

How is vector mean value calculated in higher dimensions?

In higher dimensions, the vector mean value is calculated by finding the average of the coordinates in each dimension. For example, in three dimensions, the x, y, and z coordinates are summed and divided by the total number of vectors in the set.

Can vector mean value be negative?

Yes, vector mean value can be negative if the majority of the vectors in the set have negative values. It is important to consider the direction of the vectors when interpreting the vector mean value.

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