Easy, from my recent chat with o1:
(Asked about left null space)
‘’’
these are the vectors that when viewed as linear functionals, annihilate every column of A . <…> Another way to view it: these are the vectors orthogonal to the row space.
‘’’
It’s quite obvious that vectors that “annihilate the columns” would be orthogonal to the column space not the row space.
I don’t know if you think o1 is magic. It still hallucinates, just less often and less obvious.
‘’’ these are the vectors that when viewed as linear functionals, annihilate every column of A . <…> Another way to view it: these are the vectors orthogonal to the row space. ‘’’
It’s quite obvious that vectors that “annihilate the columns” would be orthogonal to the column space not the row space.
I don’t know if you think o1 is magic. It still hallucinates, just less often and less obvious.