Three Linear Algebra Questions

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9401204 Thompson This award supports research on three areas in matrix theory. The first concerns a formula for the product of matrix exponentials the proof of which has inspired a new and deeper question. The principal investigator will work on solving this new question. The second area concerns the study of the invariants of matrix products for matrices over a noncommutative domain. The third area of research concerns the numerical range of matrices over a noncommutative domain. A natural place to begin these numerical range studies is with matrices having quaternion entries. This research is in the general area of matrix theory. A matrix is a rectangular array. Matrices can be used to represent a wide variety of situations in mathematics, engineering, statistics, physics, economics, and the life and social sciences.