positive definite symmetric matrices 中文意思是什麼
positive definite symmetric matrices
解釋
正定對稱矩陣-
Finally, when the decomposition is proceeding to a symmetric positive definite matrix, the pivot may be very small or even negative. there provided several methods to overcome this shortcoming. ( 2 ) for the block strictly diagonally dominant matrices, there proved the existence and uniqueness of the block lu decomposition and the existence of the incomplete version
（ 2 ）證明了嚴格塊對角占優矩陣塊lu分解的存在唯一性與塊不完全lu分解的存在性，以及嚴格塊對角占優矩陣與不可約塊對角占優矩陣的塊jacobi 、塊gs ，塊sor 、塊ssor等基本迭代法的收斂性。 -
The left and right inverse eigenvalue problem for symmetric positive definite and symmetric positive semidefinite matrices on subspace
子空間上的對稱正定及對稱半正定陣的左右特徵值反問題 -
A class of left and right inverse eigenvalue problems for positive definite symmetric and positive semidefinite symmetric matrices
一類對稱正定及半正定的左右逆特徵值問題 -
In chapter 2, we give some important properties of metapositive definite matrices, the expression of real and imaginary part about eigenvalues of real square matrices as well as the range of eigenvalues of real square matrices ( especially the range of their imaginary part ). on the other hand, we sum up, establish and extend some necessary and sufficient conditions of metapositive definite matrices roundly. in chapter 3, we give some important properties of complex positive definite matrices, the expression of real and imaginary part about eigenvalues of complex square matrices as well as the range of eigenvalues of complex square matrices. on the other hand, we sum up, establish and extend some necessary and sufficient conditions of complex positive definite matrices roundly. in summary, we discuss in terms of set theory the relation among real symmetric positive definite matrices, hermitian positive definite matrices and two types of generalized positive definite matrices - metapositive definite matrices and complex positive definite matrices
第一章：除引入hermite矩陣、 hermite正定矩陣和實對稱正定矩陣較重要的性質外，還建立了它們的其它一些重要性質，尤其較全面地總結和建立了它們的若干充分和必要條件；第二章：建立了亞正定陣的一些重要性質，給出了實方陣的特徵值實部和虛部的表達式，並導出了實方陣的特徵值范圍尤其是導出了其虛部范圍，同時著重較全面地總結、建立和推廣了亞正定陣的若干充分和必要條件；第三章：建立了復正定矩陣的一些重要性質，給出了復方陣的特徵值實部和虛部的表達式，並導出了復方陣的特徵值范圍，同時著重較全面地總結、建立和推廣了復正定矩陣的若干充分和必要條件；全文小結：從集合論的觀點出發，對已討論過的四類正定矩陣? ?實對稱正定矩陣、 hermite正定矩陣、亞正定矩陣和復正定矩陣之間的關系作了比較細致的論證與探討。
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