Linear Algebra Seminar

Speaker: Dr. Huajun Huang

Title: Witt's Theorem: History, Extensions, and Applications

Abstract: Let (V, b) be a metric space with a nonsingular symmetric, skew-symmetric, Hermitian, or skew-Hermitian form b over a field K of characteristic not 2. The Witt's Theorem states that any isometry between two subspaces of a nonsingular metric space may be extended to an isometry of the whole space. In this talk, I will give some extensions of Witt Theorem to handle simultaneous isometries of several subspaces. We present simple sufficient and necessary conditions for these simultaneous isometries. They are useful in investigating isometry group orbits and invariants.