The Study Of Properties Of Linear Mapping On Quaternion Matrix Space

The quaternion matrix has a good application in research of control system, figure calculation and molecular symmetry, but with the noncommutativity of multiplication, some properties are open. Linear preserving involving the algebra homomorphism and isomorphism, isometry on function space and topological mapping on continuous space, is the hot spot in matrix theory. Based on it, linear mapping preserving some properties on quaternion matrix space is described.In the first chapter, some background relevant to this paper is introduced.In the second chapter, some definitions and lemmas relevant to this paper are listed.In the third chapter, linear mapping preserving right spectrum of quaternionic matrices is given.In the fourth chapter, linear mapping preserving left spectrum of 2×2 diagonal quaternionic matrices,2×2 Hermitian quaternionic matrices are first given, then a linear mapping preserving left spectrum on complex matrices to complex matrices is given.