The CAGED system is basically a generalised theory and not usually specific to Minors. I have included them into this area just so you can get an idea of how minors are associated to majors. If you wanted to you could also make a CAGED system using Sevenths, Diminished and Augmented's and so on. I would suggest mastering the CAGED system in majors and then learn how to change every C Major, A Major, G Major, E Major and D Major chord into minors, 7th, major 7th an so on.
This is not a common shape on the guitar, it twists the finger around to get into position and I rarely see it being used in songs. So why do it? The simple fact is that it exists! so don't ignore it. Try to get use to all the common extensions, Minor, 7th, Major 7th, Minor 7th & Suspended, all around the CAGED system.
A Shape
A Minor Shaped Bar Chord
When you think about it there are 5 open chords you learn first up "A, C, D, E & G" then the most common minor chords are Am, Dm & Em. If you don't know this bar chord shape by now then it's advisable that you do, or that lack of chord knowledge will stunt your growth as a guitarist.
G Shape
G Minor Shaped Bar Chord
This is another chord shape that you will rarely come across, simply for the fact that it is not easy to play. This open chord shape won't convert directly into a bar chord because you'll simply run out of fingers. With these harder shapes just choose part of the chord and move it up the neck. For this example we will only use the lower 4 strings.
E Shape
E Minor Shaped Bar Chord
This is a common shape and the "Em" open chord should have been one of the first you would have learnt.
D Shape
D Minor Shaped Bar Chord
The most common way for anyone to learn new chords is by learning new songs. I have found that there a more beginner songs containing Am & Em rather than Dm. This shape is not as familiar to most beginner and intermediate players as the other two common minor shapes, A & E.
