# Information Operators¶

Information operators of probabilistic linear solvers.

Information operators collect information about the quantity of interest by observing the numerical problem to be solved given an action. When solving linear systems, the information operator takes an action vector and observes the tuple $$(A, b)$$, returning an observation vector. For example, one might observe the projected residual $$y = s^\top (A x_i - b)$$ with the action $$s$$.

## Classes¶

 Information operator of a (probabilistic) linear solver. Matrix-vector product $$s_i \mapsto A s_i$$ with the system matrix. Projected residual $$s_i \mapsto s_i^\top (A x_i-b)$$ of the linear system.