Abstract:
This talk will have two different parts. The first is about the
"Four Fundamental Subspaces" -- the column space and nullspace of a
matrix A and its transpose. Those are so useful in teaching and they are
equally important in applications. When A is the incidence matrix
of a graph, they lead to a key model for problems in applied mathematics
and combinatorics. We describe that model and open questions.
The second part is a question: Are random triangles acute or obtuse ?
I just discovered that Lewis Carroll (and others) asked this earlier.
There are multiple answers. We add one more.