Is it possible to extract the diagonal elements of a matrix into a vector by using matrix multiplication only? If it is possible show how ;)
I'm curious how long it will take for you guys to answer this. Btw, no element by element multiplication is allowed.
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={MMULT(horizontal,MMULT(matrix,TRANSPOSE(horizontal))}
This results in a number. The question asks for a column vector with the diagonal elements in it. ;)
Look, I don't know how to do it in excel because I refuse to lower my standards to it, but in general
Ax = b
Take a 2-by-2 matrix A, where a_ij is the ith row and jth column element (i,j =2). Then you want b = [a_11 a_22]^T (T is the transpose). In this case,
Ax = b (A^-1)Ax = (A^-1)b
hence x = (A^-1)b
So matrix A has to be invertible. If you can find the inverse of a matrix using your software, then simply multiply this inverse matrix by the vector of diagonals to get this vector x, which you need to multiply to the vector of diagonals.
That's pretty much the way to do it, but in this case I am not allowed to use any 'find' commands, nor am I able to use any other commands that create a diagonal matrix (all elements besides the diagonal are zero). I am only allowed to use the multiplication of matrices, and am constrained by the number of multiplications I can perform.
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