冪零矩陣的性質(zhì)及應(yīng)用畢業(yè)論文-wenkub
2023-07-05 06:07:05 本頁面
【正文】 分析、微分方程、力學(xué)、網(wǎng)絡(luò)等學(xué)科領(lǐng)域都與矩陣?yán)碚撚兄芮械穆?lián)系，甚至在經(jīng)濟(jì)管理、金融、保險(xiǎn)、社會(huì)科學(xué)的領(lǐng)域，矩陣?yán)碚撘灿兄种匾淖饔茫@得了許多重要的研究成果。字典關(guān)鍵詞：冪零矩陣；特征值；若爾當(dāng)形Abstract Matrix in higher algebra is an important tool to research problem,When discussing matrix multiplication of the definition of nilpotent matrix is given. In the study of matrix and learning about mathematics knowledge, often to discuss its properties. As a special matrix, nilpotent matrix in terms of matrix theory, or in the actual application has very important significance. The properties of nilpotent matrix has a lot of good, The article starting from the definition of matrix to get some simple properties, And then from different angles to dig deeper into its nature more. By the given arguments, Discussed some properties of nilpotent matrix, but also through the example is given to show its application, this is a great benefit to solve the problem of several matrix.Key words：Nilpotent matrix。我們?cè)谘芯烤仃嚰皩W(xué)習(xí)有關(guān)數(shù)學(xué)知識(shí)時(shí)，經(jīng)常要討論其性質(zhì)。冪零矩陣作為特殊的矩陣，無論在矩陣?yán)碚摲矫?，還是在實(shí)際應(yīng)用方面都有著很重要的意義。eigenvalue。近年來冪零矩陣得到了進(jìn)一步發(fā)展，在1964年Give證明了階矩陣是冪零矩陣的充要條件是，當(dāng)然還有其他衍生出來的幾個(gè)充要條件在下文中給出。2. 冪零矩陣的相關(guān)概念及簡(jiǎn)單性質(zhì)為了敘述的需要,我們首先引入冪零矩陣的相關(guān)概念. 冪零矩陣的相關(guān)概念 ，若存在正整數(shù)，使，則稱冪零矩陣。顯然，階零矩陣是特殊的冪零矩陣且其冪零指數(shù)為1。 形為階數(shù)為的矩陣稱為若爾當(dāng)塊,其中為復(fù)數(shù)。 冪零矩陣都不可逆。證明：因?yàn)闉?
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