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.
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