The most common and most likely answer to this crossword clue is the 8 letter word SUBSPACE
I've seen this crossword clue in Independent
S
U
B
S
P
A
C
E
Buddy explains!

The straight part
We know that "Part of a matrix" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case part of a matrix = subspace.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
Crossword Answer definitions
SUBSPACE noun- A subset of a space which is a space in its own right.
- Any (often unspecified) method of communicating faster than light speed.
- (BDSM) The psychological state of the submissive or "bottom" during sadomasochistic activity.