Kronecker Product Of Some Digonally Dominant Matrixs

With the rapid development of science and technology, when use the matrixtheory and method to solve the mathematic problems in the modern technologyfield, the advantages which are describing deeply and expressing succinctly arepaid attention by mathematicians. So matrix has become one of commonly usedinstruments in scitific calculate. Diagonally dominant matrix is a important classof special matrix in mathematic science and engineering application, they havemany special properties and play an important role in many areas. In the area ofdiagonally dominant matrix with the special properties of diagonally dominantmatrix, many domestic and overseas scholars have done a great of works andobtained lots of important results.In this thseis, by using the properties of Kronecker product of matrixs, com-bining with the inequalities techniques, some new judging conditions for strictα-diagonally dominant matrixs are obtained and some existed results are improved.In chapter one, we first present some background knowledge and recent worksfor diagonally dominant matrix and matrix Kronecker product specially forα-diagonally dominant matrix. Then we introduce some basic symbols and defini-tions used in this paper.In chapter two, by using the properties ofα- diagonally dominant matrix andmatrix Kronecker product and matrix Kronecker addition, combining with theinequalities techniques, some new necessary and su?cient conditions which areconcerning that two matrixs making Kronencker product or Kronecker additionremain are strictα- diagonally dominant matrix are obtained, correspondinglydicussing some concerning su?cient conditions, then some recent results are im-proved e?ectively.In chapter three, first of all, it gives a necessary condition which is concerningthat the Kronencker product of two matrixs is strictα-chain diagonally dominantmatrix, then by combining the properties ofα- chain diagonally dominant matrixand matrix Kronecker product, using with the inequalities techniques and theproperties of maximum value, some new judging conditions which are concerningthat two matrixs making Kronencker product remain are strictα-chain diagonallydominant matrix are obtained.