Crossword Genius

Sad song in Matrix about Neo's Heart (5)

Ross

I believe the answer is:

dirge

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'sad song' is the definition.
(I've seen this before)

'in matrix about neo's heart' is the wordplay.
'in' means one lot of letters goes inside another.
'matrix' becomes 'die' (I've seen this in another clue).
'about' says the letters should be written backwards.
'neo's heart' becomes 'gr' (I can't justify this - if you can you should give a lot more credence to this answer).
'gr' reversed gives 'rg'.
'die' enclosing 'rg' is 'DIRGE'.

Can you help me to learn more?

(Other definitions for dirge that I've seen before include "lamentable composition", "Threnody", "No joy in this music", "Melancholy song", "Dragging piece".)

I've seen this clue in The Sun.
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