How can a column vector be transformed into a diagonal matrix?

[MehranMo]

I think this is a pretty simple question. I need a transformation that will take a Column vector e.g.: <a,b,c> and turn it into a 3x3 matrix where a is in position 1,1 and b in position 2,2 and c in position 3,3. i.e.: a diagonal matrix.

Any help?

 

[Fredrik]

What kind of transformation? You can define the function by saying that for each i,j we define X_{ij}=\delta_{ij}x_i. (There's no summation over the repeated indices). Do you need to define the function by matrix multiplication alone, or is it OK to use addition too?

 

[I like Serena]

You could pick a 3 dimensional matrix (a 3x3x3 cube) with 1's on the main diagonal.

 

[JG89]

There is a linear isomorphism \alpha such that for any vector (a, b, c) \alpha will take (a,b,c) to the 3 by 3 matrix, whose main-diagonal entries are a, b, and c, with all other entries being 0.