"Definite" property : does that mean something "alone" or must be precedeed by "positive"

Question

I have a question about mathematical definitions.

A positive matrix is a matrix having only positive coefficient.

A definite positive matrix is a matrix that verifies $\langle x | M | x \rangle \geq 0$ (I assume working in Hilbert space for simplicity).

An inner product is positive definite if $\forall x \neq 0 \langle x | x \rangle > 0$.

My question is:

Does the term "definite" mean something in itself or it must always be preceeded/followed by an adjective like positive in those example ? In short must I consider "positive-definite" as a full word or each term has its own meaning ?

I always found confusing this vocabulary and I would like to understand the origin so maybe it will make some concept more clear in my mind.

Answer 1

This might be another illustration of the red herring principle.

Eg, a field is usually defined to have commutative multiplication, but a skew field has a non-commutative multiplication (hence is not a field).