有關(guān)對(duì)角矩陣的證明與應(yīng)用畢業(yè)論文-資料下載頁(yè)
2025-06-23 17:14本頁(yè)面
【正文】 陣在實(shí)際生活中有著廣泛的應(yīng)用，這里只是略微談一下。例1：某實(shí)驗(yàn)性生產(chǎn)線(xiàn)每年一月份進(jìn)行熟練工與非熟練工的統(tǒng)計(jì)，然后將1/6熟練工支援其他生產(chǎn)部門(mén)，其缺額由招收新的非熟練工補(bǔ)齊。新、老非熟練工經(jīng)過(guò)培訓(xùn)及實(shí)踐至年終考核有2/5成為熟練工。設(shè)第n年一月份統(tǒng)計(jì)的熟練工與非熟練工所占百分比分別為和，記成向量。（1） 求與的關(guān)系式并寫(xiě)成矩陣形式=A；（2） 驗(yàn)證，是A的兩個(gè)線(xiàn)性無(wú)關(guān)的特征向量，并寫(xiě)出相應(yīng)的特征值；（3） 當(dāng)時(shí)，求。解：（1）由題設(shè)可列出與的關(guān)系式=5/6+2/5(1/6+)。=3/5(1/6+)化簡(jiǎn)得=，于是A=。（2）令P==，則由|P|=5≠0知線(xiàn)性無(wú)關(guān)。因?yàn)锳==，故為A的特征向量，且相應(yīng)的特征值為= = = ，故為A的特征向量，且相應(yīng)的特征值為= 。（3）=A==…==由=，有A=P。于是= P ，又=1/5，故=1/5=1/5因此==。參考文獻(xiàn)[1]北京大學(xué)數(shù)學(xué)系幾何與代數(shù)教研室前代數(shù)小組. 高等代數(shù)【M】.北京：高等教育出版社，2003.[2]【M】.北京：高等教育出版社，2007.[3]【M】.北京：中央民族大學(xué)出版社，2006.[4]徐仲，【M】.西安：西北工業(yè)大學(xué)出版社，2009.Identification and application of the diagonal matrixAbstract:Diagonalization of the matrix is a reflection of an important concept matrix properties, whether for mathematics majors of Higher Algebra and not learn mathematics majors in linear algebra to learn and understand the meaning of it is necessary. This paper mainly studies the diagonalization of matrix problems, summarizes the diagonalization of matrix operations, properties, method, as well as in linear algebra and matrix diagonalization, some knowledge related to the permeability of ordinary differential equations, spatial analytic geometry problems, makes the diagonalization of matrix with understanding and a more profound understanding, which can be more flexible use of knowledge to solve related problems.Keywords: diagonalization of the matrix eigenvalue eigenvector
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