Q:

Can we have a perfect cadence in a minor key?

I understand that, at least in the context of using a major scale, a perfect cadence is V-I. That is, if I were playing a piece in C major, I could play a chord similiar to the G major triad followed by a chord similar to the C major triad.*
What about in a minor key? If my piece is in the key of A minor, would I achieve a perfect cadence by playing an E major chord followed by an A major chord? Or would I instead have to play an E minor chord followed by an A minor chord?

Footnotes:
*I know that some theorists say that its not a perfect cadence unless the highest note of the I chord is the tonic note. For my purposes, however, I'm not using that convention.

A:

For starters, we can call this cadence an authentic cadence, since by definition that is understood to be a V–I motion. The highest note distinguishes between perfect and imperfect authentic cadences.
With that said, an authentic cadence is simply a root-position dominant moving to a root-position tonic. Although the dominant chord must be major, the tonic chord can be major or minor and still be an authentic cadence.
In fact, the quality of the tonic chord can be opposite of what you expect and still be considered a perfect authentic cadence. This is pretty intuitive in minor; ending on a major tonic almost makes the cadence more final. But even in major, if we suddenly cadence onto a minor tonic, this is still a perfect authentic cadence. (Although we'd certainly want to clarify that it's attenuated in some way with the unexpected shift to minor.)

A:

Americans seem to call a 'Perfect cadence' an 'Authentic cadence'.   And there's this new thing a 'Perfect Authentic cadence'.   OK, whatever.  Dominant to tonic.  Perfect (or Authentic) cadence.
This is a Common Practice, Functional Harmony thing.  A world where minor scales are Harmonic (at cadence points, at any rate), dominant chords are major and thus include the leading note.   But tonics can be minor.  The urge to 'regularise' a final cadence in a minor key with a Tierce di Picardie was not always followed!
So, G7 - C is a Perfect cadence.  So is E7 - Am.  And we don't have to change that to E7 - A in order to make it one.
Em - Am  does happen, and it has every right to be considered some sort of a cadence.  But it isn't a Perfect one.

