Question about a matrix of vector element ratios

In summary, a matrix of vector element ratios is a mathematical representation of the relationship between two sets of vectors. It is useful for comparing the relative proportions of different vectors and identifying patterns or trends within the data. However, it can only be created for vectors of the same length to ensure accurate comparison. A matrix of vector element ratios compares the values of two entire vectors, while a matrix of element-wise ratios compares the values of individual elements within a vector. A value of 1 in the matrix indicates that the two corresponding elements in the vectors have the same value, while a value greater than 1 or less than 1 indicates a difference in value between the elements of the vectors.
  • #1
enfield
21
0
if I have square matrix A whose decimal elements [tex] a_{i,j} = \frac{v_i}{v_j} [/tex] how do I find (or approximate) the vector that would produce the matrix elements. what's a good way to do that?

i guess you can scale the vector however you want and it'll still produce the same matrix..

thanks.
 
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  • #2
Consider what summing the matrix elements over i produces.
 

1. What is a matrix of vector element ratios?

A matrix of vector element ratios is a mathematical representation of the relationship between two sets of vectors. It is created by dividing the values of one vector by the corresponding values in another vector, resulting in a matrix of ratios.

2. How is a matrix of vector element ratios useful?

A matrix of vector element ratios is useful for comparing the relative proportions of different vectors. It can also be used to identify patterns or trends within the data.

3. Can a matrix of vector element ratios be created for vectors of different lengths?

No, a matrix of vector element ratios can only be created for vectors of the same length. This ensures that each element in one vector has a corresponding element in the other vector for accurate comparison.

4. What is the difference between a matrix of vector element ratios and a matrix of element-wise ratios?

A matrix of vector element ratios compares the values of two entire vectors, while a matrix of element-wise ratios compares the values of individual elements within a vector.

5. How can a matrix of vector element ratios be interpreted?

A value of 1 in the matrix indicates that the two corresponding elements in the vectors have the same value. A value greater than 1 indicates that the element in the first vector is larger than the corresponding element in the second vector, and a value less than 1 indicates that the element in the first vector is smaller than the corresponding element in the second vector.

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