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Let where is an-dimensional-vector space. Then is guaranteed to have an eigenvalue when

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Let<br><img src='https://www.fatskills.com/images2/GradExams/9D0E9491-F04D-403B-A77D-0DAFB84115B5.png' height='20' width='102'/> where<br><img src='https://www.fatskills.com/images2/GradExams/46966CA9-BBE0-4719-A5E2-76FC70B11887.png' height='15' width='14'/> is an<br><img src='https://www.fatskills.com/images2/GradExams/4B83BC74-AC32-41F5-91EC-6DF668CA2B94.png' height='10' width='11'/>-dimensional<br><img src='https://www.fatskills.com/images2/GradExams/C50F7AE8-4C1A-4A2E-A571-72CCDD0964CC.png' height='14' width='14'/>-vector space. Then<br><img src='https://www.fatskills.com/images2/GradExams/38409966-4AFF-447C-8374-D83A9632557A.png' height='14' width='14'/> is guaranteed to have an eigenvalue when





 
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