  Energy conditions for matter fields are comprehensively investigated in
arbitrary $n(\ge 3)$ dimensions without specifying future and past directions
locally. We classify an energy-momentum tensor into $n$-dimensional
counterparts of the Hawking-Ellis type I to IV, where type III is defined by a
more useful form than those adopted by Hawking and Ellis and other authors to
identify the type-III energy-momentum tensor in a given spacetime. We also
provide necessary and sufficient conditions for types I and II as inequalities
for the orthonormal components of the energy-momentum tensor in a canonical
form and show that types III and IV violate all the standard energy conditions.
Lastly, we study energy conditions for a set of physically motivated matter
fields.
