An equivalent formulation in terms of linear algebra is the following.

These are exactly equivalent formulations, merely using different notation for the dot product.

The theory has an equivalent formulation in terms of von Neumann algebras.

For more properties and equivalent formulations, see the separate entry product topology.

The Schrödinger picture for time evolution has several mathematically equivalent formulations.

The following equivalent formulation of Arrhenius' greenhouse law is still used today:

The amenability property has a large number of equivalent formulations.

The problem admits a number of equivalent formulations.

An equivalent formulation of the theorem is the following.

The above model has an equivalent formulation as a latent-variable model.