Dispersion operator in quantum mechanics

[Ananthan9470]

I am a beginner in quantum mechanics and I am confused about the operator ΔA defined to be ΔA Ξ A - <A>. Can someone please tell me how to interpret <A>? From what I can understand, <A> is the expectation value and is defined to be <Ψ|A|Ψ>. But that is just a scalar correct? How do subtract a scalar from a matrix; do you just do the subtraction element wise from the matrix? And what does all this mean?

 

[blue_leaf77]

The matrix representation of a scalar is the scalar itself multiplied by an identity matrix.