求逆矩阵的几种方法

矩阵是线性代数中的主要研究对象与研究工具,而逆矩阵是矩阵理论中的一个非常重要的概念,如何判断一个矩阵是否可逆以及如何求矩阵的逆矩阵就显得非常重要。求逆矩阵方法很多,本文归纳了如下几种:定义法;利用伴随矩阵求逆法;利用伴随矩阵求逆法的推论求逆;利用逆矩阵的性质求逆法;利用矩阵的初等变换求逆;分块对角阵求逆法。     

矩阵相似的相关研究

矩阵是高等代数中的一个重要分支,它在其他社会科学、自然科学、工程技术等领域都有着广泛应用。矩阵相似是矩阵中很重要的一种关系,矩阵的相似涉及到矩阵,矩阵可逆,同时矩阵相似可应用于两分块矩阵中和求可逆矩阵中。在此主要介绍矩阵的相似性,两个方块矩阵的相似,矩阵相似的判别方法,以便我们能对矩阵的相似有进一步的了解。     

大型基因组亲缘矩阵求逆算法的优化研究

基因组选择常用的评估方法GBLUP和ssGBLUP都涉及到基因组亲缘矩阵的求逆,而大规模矩阵求逆运算非常耗时。本研究以提高大型基因组亲缘矩阵求逆运算的效率为目的。本研究通过真实数据和模拟数据构建基因组亲缘矩阵,引入Intel MKL矩阵函数,以减少迭代次数（方法1）和重复分块（方法2）两种方式改良分块迭代求逆算法,编程实现算法并在台式电脑和服务器上测试计算时间。结果表明,利用方法1计算4 000×4 000的基因组亲缘矩阵逆矩阵时,与MKL库函数的加速比为0.898。而16 000×16 000矩阵的计算速度为MKL库函数的1.006倍。利用方法2计算4 000×4 000矩阵的运算速度是MKL库函数的1.084倍;而在更大型的128 000×128 000基因组亲缘矩阵求逆运算时,该方法与MKL直接求逆函数的加速比为1.805倍。相比于MKL直接求逆函数,改进后的两种方法在效率上有一定程度的提升。     

大型基因组亲缘矩阵求逆算法的优化研究

基因组选择常用的评估方法GBLUP和ssGBLUP都涉及到基因组亲缘矩阵的求逆,而大规模矩阵求逆运算非常耗时。本研究以提高大型基因组亲缘矩阵求逆运算的效率为目的。本研究通过真实数据和模拟数据构建基因组亲缘矩阵,引入Intel MKL矩阵函数,以减少迭代次数(方法1)和重复分块(方法2)两种方式改良分块迭代求逆算法,编程实现算法并在台式电脑和服务器上测试计算时间。结果表明,利用方法1计算4 000×4 000的基因组亲缘矩阵逆矩阵时,与MKL库函数的加速比为0.898。而16 000×16 000矩阵的计算速度为MKL库函数的1.006倍。利用方法2计算4 000×4 000矩阵的运算速度是MKL库函数的1.084倍;而在更大型的128 000×128 000基因组亲缘矩阵求逆运算时,该方法与MKL直接求逆函数的加速比为1.805倍。相比于MKL直接求逆函数,改进后的两种方法在效率上有一定程度的提升。     

求解矩阵方程AX=B的新视角

线性方程组是线性代数的一条主线,本文从解线性方程组的角度出发,绕过初等方阵的概念及其理论,给出了求解矩阵方程AX=B通解的方法,从这个角度出发,无论方阵A是否可逆,都可以判断矩阵方程是否有解。     

分子亲缘系数矩阵的EXCEL计算程序

本文通过VBA语言编程，实现了分子亲缘系数矩阵及其逆阵计算的程序设计，提高了数据处理的准确性。尤其是该程序借助于已在国内广泛使用的Excel，使广大基层技术人员采用最佳线性无偏预测(BLUP)法进行家畜育种值评定更加方便可行。     

循环矩阵的相关介绍

特殊矩阵在代数学中占有非常重要的地位,本篇文章主要介绍了一类特殊矩阵,循环矩阵的一些相关知识与重要性质,以及它现今的发展概况。     

选修4-2《矩阵与变换》与《高等代数》

矩阵是数学中重要的基本概念,能将代数、几何紧密的联系在一起,并且在解决初高中数学问题上也应用十分广泛。在高中数学选修4—2《矩阵与变换》这本书中,第一次将矩阵的相关概念介绍给学生。由于这本书是选修教材,与高考的考点也没有联系,而高考是一个学生人生机遇的重大转折,同时也是衡量一个学校教学质量的重要标准。很多学校在课程安排进度中,就没有更多的时间去讲解与高考联系不大的选修系列。就这样学生与矩阵知识擦肩而过,而高中涉及的简单矩阵知识就可以解决高中的很多问题,如用矩阵证明等式、用矩阵分解因式、矩阵在解析几何中的应用、关于消元法与解的结构、几个平面共点、共线、平行与重合的问题、利用矩阵的秩判断两直线位置关系、利用矩阵求最大公因式等。并且这本书的编写对大学必修《高等代数》教材的理解也作了铺垫作用,对未来的学习也有很多帮助。两本教材在矩阵的变换、矩阵的逆、特征值与特征向量上联系十分紧密。它们的都有对矩阵知识的描述,但引入方式和知识所涉及到的范围却大不相同。     

区间对角占优矩阵的判定

本文引入区间对角占优矩阵的定义,讨论了区间对角占优矩阵的性质,给出了区间对角占优矩阵的判定方法 。     

浅谈矩阵在数学建模中的应用

矩阵作为一种认识复杂事物的简捷工具已经被广泛应用在各个学科领域中,在数学建模中也有许多应用.本文就数学建模中使用矩阵的情况做一些举例、小结,最后给出一个典型的数学模型.     

有机生态型无土基质对披碱草苗期生长的影响

有机生态型无土栽培基质配方的研究是未来无土栽培基质配方研究新的热点.在总结前人基质配方基础上,将草炭、草木灰、枯落物、腐殖质按照一定的体积比进行混合并加入适量聚丙烯酰胺型小颗粒保水剂作为栽培基质来代替土壤,配制出4种有机生态型无土栽培基质.加入基肥后,用披碱草(Elymus dahuricus)作为试验牧草,筛选出最适...     

Estimates of genetic variance and variance of predicted genetic merits using pedigree or genomic relationship matrices in six Brown Swiss cattle populations for different traits

The amount of variance captured in genetic estimations may depend on whether a pedigree‐based or genomic relationship matrix is used. The purpose of this study was to investigate the genetic variance as well as the variance of predicted genetic merits (PGM) using pedigree‐based or genomic relationship matrices in Brown Swiss cattle. We examined a range of traits in six populations amounting to 173 population‐trait combinations. A main aim was to determine how using different relationship matrices affect variance estimation. We calculated ratios between different types of estimates and analysed the impact of trait heritability and population size. The genetic variances estimated by REML using a genomic relationship matrix were always smaller than the variances that were similarly estimated using a pedigree‐based relationship matrix. The variances from the genomic relationship matrix became closer to estimates from a pedigree relationship matrix as heritability and population size increased. In contrast, variances of predicted genetic merits obtained using a genomic relationship matrix were mostly larger than variances of genetic merit predicted using pedigree‐based relationship matrix. The ratio of the genomic to pedigree‐based PGM variances decreased as heritability and population size rose. The increased variance among predicted genetic merits is important for animal breeding because this is one of the factors influencing genetic progress.     

Calculation of identity‐by‐descent probabilities of short chromosome segments

For some purposes, identity‐by‐descent (IBD) probabilities for entire chromosome segments are required. Making use of pedigree information, length of the segment and the assumption of no crossing‐over, a generalization of a previously published graph theory oriented algorithm accounting for nonzero IBD of common ancestors is given, which can be viewed as method of path coefficients for entire chromosome segments. Furthermore, rules for setting up a gametic version of a segmental IBD matrix are presented. Results from the generalized graph theory oriented method, the gametic segmental IBD matrix and the segmental IBD matrix for individuals are identical.     

狂犬病病毒BD-06株基质蛋白的原核表达、纯化及其多克隆抗体的制备

本研究旨在获得抗狂犬病病毒M蛋白的多克隆抗体,为进一步研究M蛋白功能提供材料。本试验以狂犬病病毒BD06毒株为模板克隆M基因序列,将其克隆至原核表达载体pET28a;经酶切和测序鉴定,M蛋白基因序列已正确插入表达载体pET28a;以表达载体pET28a-M转化E.coli Rosetta株,并以0.5 mmol/L IPTG诱导,结果表达出27 ku左右的M蛋白;将诱导表达的蛋白质回收纯化,以纯化的M蛋白多次免疫兔子制备多克隆抗体;Western blotting分析和间接免疫荧光分析结果表明,制得的抗体与病毒能够反应,运用制得的多克隆抗体定位了基质蛋白在感染狂犬病病毒的BHK-21细胞中的位置。结果表明成功制得了抗狂犬病病毒M蛋白的多克隆抗体,为研究狂犬病病毒M蛋白功能奠定了基础。     

Effects of platelet rich plasma and acellular bone marrow on gene expression patterns and DNA content of equine suspensory ligament explant cultures

REASONS FOR PERFORMING STUDY: Suspensory ligament (SL) desmitis is a common source of lameness. The results of this study will determine if blood-derived products stimulate SL matrix synthesis and have potential as regenerative therapies for SL desmitis OBJECTIVES: To determine if various blood-based biological products including plasma, blood, PRP, platelet poor plasma (PPP) and ABM aspirate stimulates anabolic and/or catabolic pathways in suspensory ligaments (SL). METHODS: The body of the SL was harvested from 6 horses and used to establish explant cultures. Explants were cultured in plasma, blood, PRP, PPP or ABM at concentrations of 10, 50 or 100%. Anabolic responses were assessed by use of quantitative PCR for collagens type I and III, cartilage oligomeric matrix protein (COMP) and decorin. Total DNA and collagen protein content were also measured. Catabolic reactions were measured by quantitative PCR for matrix metalloproteinases 3 and 13 (MMP-3, MMP-13). Results: Acellular bone marrow aspirate at 100% stimulated decorin and COMP mRNA synthesis more than all other treatments at all concentrations. No treatment at any concentration stimulated the catabolic gene MMP-13; only 50% ABM stimulated MMP-13 mRNA expression. CONCLUSIONS: Acellular bone marrow is indicated, and might be preferred to plasma, blood or PPP, as a blood-based biological source for SL tissue regenerative therapy. Long-term, placebo controlled case studies are indicated to determine if ABM aids in recovery from SL desmitis. POTENTIAL RELEVANCE: Bone marrow aspirate is an autogenous, readily available biological source for SL regenerative therapy where the aim is to stimulate matrix synthesis.     

Computing inbreeding coefficients and the inverse numerator relationship matrix in large populations of honey bees

The inbreeding coefficients are considered in breeding decisions, and the inverse numerator relationship matrix A ^?1 is a prerequisite for breeding value estimation. Polyandry and haploid males are among the specifics of relationships between honey bees. Brascamp and Bijma (2014) averaged out the manifold possible relationships among honey bees that appear to have the same parents in a pedigree and assigned a single entry in A to animals that behave as a unit, for example, the workers of a hive. Their methods of calculation connected full‐sibs in the variance matrix of the Mendelian sampling terms D , via nonzero off‐diagonal elements. This impedes the inversion of A and the closely connected calculation of inbreeding coefficients, because efficient algorithms for this task take D to be a diagonal matrix. Memory limitations necessitate their use for large data sets. We adapted the quickest of them to the block diagonal matrix D , that is postulated for the honey bee. To our knowledge, the presented algorithm is the first one that facilitates the method of Brascamp and Bijma (2014) on large data sets.     

一种适用于单胎动物多品种选择的基因组关系矩阵

旨在提出一种新型基因组关系矩阵并验证其在多品种联合群体中的模拟应用效果。本研究利用QMsim软件模拟牛的表型数据和基因型数据;利用Gmatrix软件构建常规G阵;利用R语言构建新型G阵,新型G阵在常规G阵的基础上,将多品种联合群体的非哈代-温伯格平衡位点考虑在内;利用DMU软件使用“一步”法模型计算基因组估计育种值（estimated genomic breeding value,GEBV）;比较不同情况下使用两种G阵的GEBV预测准确性。结果表明,在不同遗传力及QTL数下,不对新型G阵使用A₂₂阵加权就能达到常规G阵使用A₂₂阵加权时的GEBV预测准确性。在系谱部分缺失时,新型G阵不加权较常规G阵加权时GEBV预测准确性高。证明,在系谱有部分缺失时,新型G阵对多品种GEBV的预测有一定优势。     

饲料制粒机环模结构强度分析

环模是压制颗粒饲料的核心工作部件,其失效形式主要是磨料磨损以及因为强度不足引起的疲劳破坏。通过对环模及模孔进行受力分析及应力计算,建立了环模结构参数与应力之间的映射关系,为改善环模结构,延长环模的使用寿命提供了依据。