Contemplating x2 = -1 where x is a square matrix, and the interesting structures that ensue
Using familiar and elementary ideas from linear algebra and calculus, we'll be led by the suggestive title above. The numeral 1 literally means an identity matrix, and our contemplation will include exploring the questions
- when are there solutions, and
- what do they look like, both individually and collectively?
This is all the first step in a vast area of active mathematical research, with important open problems, on the study of certain higher dimensional shapes called manifolds. I'll share some perspectives on this at the end. It's best to come with a curious and open mind!
X2=x1x2x3x42= 1001
Find X.
Monday, April 17
4pm
Williams 323
sponsored by the Math Department Colloquium series, lead-in to the Pi Mu Epsilon Induction ceremony. Contact: tgalanthay@ithaca.edu (Prof. Ted Galanthay)