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...
 

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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