例句與造句

1. in this dissertation, we systematically discuss the fundamental properties and the necessary and sufficient conditions of 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 . finally, we discuss the relation among these four types of positive definite matrices
   本論文比較系統(tǒng)地研究了實對稱正定矩陣、hermite正定矩陣和兩類廣義正定矩陣??亞正定矩陣和復正定矩陣的基本性質尤其是它們的若干充分和必要條件，最后還討論了這四類正定矩陣之間的關系。
2. 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(yōu)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(yōu)矩陣與不可約塊對角占優(yōu)矩陣的塊jacobi、塊gs，塊sor、塊ssor等基本迭代法的收斂性。
3. 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，給出了實方陣的特征值實部和虛部的表達式，并導出了實方陣的特征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，給出了復方陣的特征值實部和虛部的表達式，并導出了復方陣的特征值范圍，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(fā)，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。
4. It's difficult to find symmetric positive definite matrix in a sentence. 用symmetric positive definite matrix造句挺難的