If I understand right, you’re saying that there’s an interpretation in terms of the geometry of the T transformation, of subtracting this diagonal matrix from T. Multiplication of matrices is composition of transformations, I get that, but I’m not so sure what adddition/subtraction is.
Yes, that's right. Addition is just applying the transformations separately to the same vector and adding the result. So what this is saying is that if you apply λI to a vector in that particular direction, then there is nothing left to add to get the effect of T.
Ideally you would like to do this for all n directions of space, and that way you completely describe what T does in simpler terms: it just stretches things differently in different directions. It's not always possible though. The matrices that allow this are called diagonalizable and the process of finding the stretch factors (eigenvalues) is called diagonalization.
Just a caveat: if an eigenvalue is complex, the effect is not as simple as a stretch, but the interpretation is very similar.
> So, when you took the effect of λI from T,
If I understand right, you’re saying that there’s an interpretation in terms of the geometry of the T transformation, of subtracting this diagonal matrix from T. Multiplication of matrices is composition of transformations, I get that, but I’m not so sure what adddition/subtraction is.