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?