It means at least:
1. having a zero inner product
2. (a square matrix) that is the inverse of its transpose
3. linear transformation that preserves angles
4. statistically independent
But you are correct, sir ;-)
Used to describe two things that are independent of each other. One does not imply the other.
"Common sense and intelligence are orthogonal. I've seen plenty of smart people with no common sense."
It means at least:
1. having a zero inner product
2. (a square matrix) that is the inverse of its transpose
3. linear transformation that preserves angles
4. statistically independent