A major 13th chord

Amaj13 chord for piano with keyboard diagram.
Explanation: The A major thirteenth is a six-note chord (the 11th, D in the case of Amaj13, is normally excluded). For practical reasons the chord is normally played with omitted notes and/or inverted. It is often abbreviated as Amaj13 (not to be confused with A13).
Omissions: Amaj13(no5): A - C# - G# - B - F#, Amaj13(no9): A - C# - E - G# - F#.
Theory: The A major thirteenth chord is constructed by extending the major eleventh chord with a major thirteenth note.

Amaj13

Amaj13 chord diagram diagram
Notes: A - C# - E - G# - B - F#

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Amaj13 inversions and voicings

Amaj13/G# chord diagram
Notes: G# - C# - E - F# - A
One of many possible inversions (Amaj13/G# with the 9th and the 11th omitted)

Amaj13 chord vocing diagram
Notes: A - G# - C# - F#
Two-hand voicing

A chord categories

A Am A7 Am7 Amaj7 AmM7 A6 Am6 A6/9 A5 A9 Am9 Amaj9 A11 Am11 Amaj11 A13 Am13 Amaj13 Aadd A7-5 A7+5 Asus Adim Adim7 Am7b5 Aaug Aaug7