Thread: [SOLVED] matrix manipulation

hi everyone,

I have a vector u=(x y z) and I would like to transform it (by some linear manipulations) into the following matrix:
(x 0 0)
(0 y 0)
(0 0 z)

in matlab notation: [x 0 0; 0 y 0; 0 0 z]

Concretely I would like to find some matrices A and B, for example, such that:
[x 0 0; 0 y 0; 0 z 0]=A*[x y z]*B

I know that there exists the function diag() in matlab but I would like to use some linear relations to build such a matrix.

Is there somebody that could help me?


Thank you very much

JC

Originally Posted by jcrennes2

hi everyone,

I have a vector u=(x y z) and I would like to transform it (by some linear manipulations) into the following matrix:
(x 0 0)
(0 y 0)
(0 0 z)

in matlab notation: [x 0 0; 0 y 0; 0 0 z]

Concretely I would like to find some matrices A and B, for example, such that:
[x 0 0; 0 y 0; 0 z 0]=A*[x y z]*B

I know that there exists the function diag() in matlab but I would like to use some linear relations to build such a matrix.

Is there somebody that could help me?


Thank you very much

JC

It cannot be done. The reason is this

Theorem: The rank of matrix is less than or equal to the rank of either or

is a 1x3 matrix of rank 1.

is a matrix of rank 3 (assuming the diagonal entries are non-zero).

Because of the theorem, there is no series of matrices you can multiply by to increase the rank from 1 to 3. After every multiplication, the rank will be less than or equal to 1.