Hi all;

I have a strange problem: I know exactly what I want multiplied and added, but I'm not sure how to write it as a formula.

I have a vector transformation which is expressed as the sum of two products:

a) a product of the original vector (let's call it

) by a scalar, say

b) a product of the original vector by a square matrix, say

So the whole transformation is

The scalar

is a scalar product of two other things, one of which is a row vector, the other a column vector:

Now I would like to express the entire transformation as a matrix product:

and I am in trouble writing the formula for

, because if I write

then I am adding a scalar to a matrix (

), which seems incorrect to me.

On the other hand, if I write

, where

is the identity matrix (ones on the diagonal, zeros elsewhere) of suitable size, it looks weird and redundant, if not silly, given that matrix multiplication is associative, and

.

Any ideas how I can write the formula for A?