The discussion revolves around proving that for a given nxn matrix A, where A^2=0, the column space of A (Col(A)) is a proper subset of the null space of A (Nul(A)). Participants express confusion regarding the definitions and implications of the terms involved in the problem.
The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the need to prove the existence of elements in Nul(A) that are not in Col(A), but there is no consensus on the assumptions or the approach to take.
Participants note that the problem may require clarification on whether A is a non-zero matrix, which could affect the proof. There is also some confusion about the terminology used, particularly regarding the terms "kernel" and "column space."
)tiny-tim said:hi junsugal!
(do you mean Ker(A)? it's spelled "kernel", not "colonel" … a kernel is the soft part inside the shell of a nut!
it means you have to prove that there exists an x such that x is in Nul(A) but not Col(A)
(i think the question should have stipulated that A is non-zero)
junsugal said:
junsugal said: