Historical basis for: measurement <-> linear operator?

[Stephen Tashi]

What is the history of the concept that a measurement process is associated with a linear opeartor? Did it come from something in classical physics? Taking the expected value of a random variable is a linear operator - is that part of the story?

 

[PaleMoon]

I thind that it began with Heisenberg's matrix mechanics.

 

[PaleMoon]

in 1925 people were mainly interested in the way things add (like waves)
heisenberg faced another problem with spectrum rays. there was an addition rule for energy but
no composition rules for the rays. the only thing that seemed real for him were the transitions (they can be observed) and he had doubts about tbe observability of something else. a matrix with its non diagonal terms describes possible transitions. he invented matrix multiplication and found the composition rule for transitions.
hilbert spaces are in the tradition of dirac and schroedinger
c* algebras, povm etc are in the tradition of Heisenberg.