Is it possible to extract the diagonal elements of a matrix into a vector?

In summary, extracting the diagonal elements of a matrix into a vector using only matrix multiplication is possible by implementing a sequence of matrix multiplies and adds. This involves getting one diagonal element into a 1x1 matrix and "expanding" it into the correct position in the vector, repeating and adding these steps. It may also be possible to incorporate these steps into a larger matrix multiplication operation, potentially requiring matrices with dimensions of N2 or N3 for a given matrix of order N.
  • #1
7Deuce
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Is it possible to extract the diagonal elements of a matrix into a vector??

Is it possible to extract the diagonal elements of a matrix into a vector USING ONLY MATRIX MULTIPLICATION? So no element by element multiplication, and no diag commands.

(This will eventually be implemented in MATLAB, but I am required to only use matrix multiplication, so no commands)

Is it even possible?

Thanks in advance.
 
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  • #2


You can do it with a sequence of matrix multiplies and adds.

Think about how to get one diagonal element into a 1x1 matrix, and then how to "expand" the 1x1 matrix into the right place in a vector. Repeat and add...

Possibly you combine all those steps part of a bigger matrix multiply operation (I'm speculating here) If the given matrix is order N, you might need matrices with dimensions of N2 or even N3...
 

Related to Is it possible to extract the diagonal elements of a matrix into a vector?

1. Can diagonal elements of a matrix be extracted into a vector?

Yes, it is possible to extract the diagonal elements of a matrix into a vector.

2. How can I extract the diagonal elements of a matrix into a vector?

To extract the diagonal elements of a matrix into a vector, you can use a built-in function or write a custom code that loops through the matrix and extracts the diagonal elements into a vector.

3. What is the purpose of extracting diagonal elements into a vector?

Extracting diagonal elements into a vector can be useful for performing operations on the diagonal elements separately, or for converting a matrix into a diagonal matrix.

4. Can the extraction of diagonal elements into a vector alter the original matrix?

No, extracting diagonal elements into a vector does not alter the original matrix. It only creates a new vector with the extracted elements.

5. Are there any limitations to extracting diagonal elements into a vector?

The main limitation is that the matrix must be a square matrix in order for the diagonal elements to be extracted into a vector. Additionally, the size of the vector will be equal to the number of rows or columns in the matrix.

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