one is scalaer and other is operatorrr

As it is defined in Wikipedia, Ricci curvature is a linear operator on tangent space at a point. But what is the definition of Ricci operator?

Ricci tensor is a linear form 

can you make it more clear to me ?

If Ric denotes the Ricci tensor, then the Ricci operator Q can be defined as g(Q(X),Y)=Ric(X,Y). Clearly, once you know the Ricci operator Q you can obtain all Ricci curvature Ric(X,X). 

Conversely, if you apply polarization to Ricci curvature, you can recover the Ricci tensor, and hence the Ricci operator Q. In this sense, you cannot say that Ricci operator Q is weaker case of Ricci curvature.

Dear sir,

Thank you for your valuable comment, but still i have some doubts related to that

1. From some sourse on internet I have studied that "if one can be obtained from another and primal cannot be obtained from the later, then it is a case of strictly weaker and strictly stronger ". What you say ?

2. If it is not so or whatever, can we say that ricci operator Q is weaker case of Ricci tensor ? 

What I said in my earlier comment is that, for a Riemannian manifold, kwoning the Ricci operator Q is equivalent to knowing Ricci tensor.

Thank you so much sir.