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square matrix 【數學】方陣。

square measure

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,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。

In this thesis , we study some open problems and conjectures about the linear complementarity problem . it consists of the next three aspects : firstly , we study murthys “ open problem whether the augmented matrix is a q0 - matrix for an arbitary square matrix a , provide an affirmable answer to this problem , obtain the augmented matrix of a sufficient matrix is a sufficient matrix and prove the graves algorithm can be used to solve linear complementarity problem with bisymmetry po - matrices ; secondly , we study murthys “ conjecture about positive semidefinite matrices and provide some sufficient conditions such that a matrix is a positive semidefinite matrix , we also study pang ' s conjecture , obtain two conditions when r0 - matrices and q - matrices are equivelent and some properties about e0 q - matrices ; lastly , we give a counterexample to prove danao ' s conjecture that if a is a po - matrix , a e “ a p1 * is false , point out some mistakes of murthys in [ 20 ] , obtain when n = 2 or 3 , a e “ a p1 * , i . e . the condition of theorem 3 . 2 of [ 25 ] that a p0 can be deleted and obtain a e “ a is an almost e - matrix if a is a co - matrix or column sufficient matrix 本文分為三個部分,主要研究了線性互補問題的幾個相關的公開問題以及猜想: ( 1 )研究了murthy等在[ 2 ]中提出的公開問題,即對任意的矩陣a ,其擴充矩陣是否為q _ 0 -矩陣,給出了肯定的回答,得到充分矩陣的擴充矩陣是充分矩陣,并討論了graves算法,證明了若a是雙對稱的p _ 0 -矩陣時, lcp ( q , a )可由graves算法給出; ( 2 )研究了murthy等在[ 6 ]中提出關于半正定矩陣的猜想,給出了半正定矩陣的一些充分條件,并研究了pang ~ -猜想,得到了只r _ 0 -矩陣與q -矩陣的二個等價條件,以及e _ 0 q -矩陣的一些性質; ( 3 )研究了danao在[ 25 ]中提出的danao猜想,即,若a為p _ 0 -矩陣,則,我們給出了反例證明了此猜想當n 4時不成立,指出了murthy等在[ 20 ]中的一些錯誤,得到n = 2 , 3時,即[ 25 ]中定理3 . 2中a p _ 0的條件可以去掉。

The rudder roll damping system is just the system whose controlled object is not square matrix . the input is rudder - order and the outputs are the roll angle and the heading angle . the input controls the two outputs 舵阻搖系統正是被控對象為非方陣的系統,它通過輸入_ r (舵令)來控制輸出(橫搖角)和(首向角) 。

However , it is very difficult that the controller is designed when the controlled object is not square matrix , because it is involved in the pseudo inverse of matrix 但是,在被控對象為非方陣的系統中,由于求解控制器時涉及到矩陣求偽逆問題,很大程度上增加了此課題的難度,故此種情況下的閉環增益成形算法未被提出。

Q9 has a number of distinct advantages in penetrating mobile telephone s market through its application of matrix mapping system ( q9 cis ) by employing a three by three square matrix 九方獨有的全方位搜索系統是透過三乘三正方矩陣的使用,將能促使公司進一步滲透流動電話市場。

Q9 has a number of distinct advantages in penetrating mobile telephone s market through its application of matrix mapping system q9 cis by employing a three by three square matrix 九方獨有的全方位搜索系統是透過三乘三正方矩陣的使用,將能促使公司進一步滲透流動電話市場。

The application of the control algorithm to the siso system , the unstable process and the mimo system whose controlled object is square matrix has been affirmed fully 閉環增益成形算法在siso系統、非穩定過程和被控對象為方陣的mimo系統中的應用已被充分肯定。

The control algorithm of closed - loop gain shaping when the controlled object is not square matrix in the simo system is developed in this thesis 本文提出了單輸入多輸出( simo )系統即被控對象為非方陣情況下的閉環增益成形控制算法。

The identity matrix of dimension n is a square matrix which contains ones along the diagonal and zeros in all other positions 使這個n維矩陣的一個對角線上的元素為1 ,而其他位置為0 。

Standard power method in evaluating all the maximum modulus eigenvalues of square matrix and associated eigenvectors 階實方陣的任意個模最大的特征值及其相應特征向量的規范化冪法

The matrices in cwmtx include vectors and square matrices , where vectors include space vectors and quaternions Cwmtx中的矩陣包括向量和方陣,其中向量包括空間向量和四元數。

A new method on the decision of positive definite quadratic form using the real square matrices 利用實方陣判定二次型正定性的新方法

Square matrix root operation 方陣的開方運算