Wigner-Eckart theorem and "reduced matrix element" Hello, I am studying the Wigner-Eckart theorem and I have found some difficulties understanding the reduced matrix element of a spherical tensor. In fact, a spherical tensor is commonly defined through its transformation properties, and I imagine it as a "vector of angular operators": the Wigner-Eckart theorem evaluates one matrix element of a component of this vector. However, I cannot understand the meaning of the reduced matrix element involved in the expression of the theorem. Please, could you explain to me the "idea" behind it, or where is the mistake in my idea of spherical tensors (if there is a mistake)? Thank you very much for your help!