Can anyone explain to me why a cycle basis hones the properties of a matroid? Especially points 2 & 3.
How can a subset of I also be a member of I? Isn't a cycle basis supposed to be consisted of cycles and cycles only? If the cycle basis consisted a triangle, wouldn't a subset of the triangle become an edge? And by point 2 am I supposed to say that the edge is also a member of I?
I would really appreciate it if anyone can use a square or pentagon graph to explain, cuz my mind is really messed up...
Thanks in advance.