Science:Math Exam Resources/Courses/MATH307/April 2010/Question 02 (c)
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Question 02 (c) 

A real matrix is brought into its Jordan canonical form
by a matrix , i.e. . Answer the questions below, substantiate all your statements. (c) What is the dimension of the kernel of (I being the 5x5 identity matrix)? 
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Hint 

Science:Math Exam Resources/Courses/MATH307/April 2010/Question 02 (c)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The kernel of where Since , then . This means to find , we just need to find the dimension of the nullspace of A with the eigenvalue 1. From matrix B, we can see that the eigenvalue 1 appears twice, and that they are not from the same Jordan block. If they were from the same Jordan block, then there would be a 1 shown at entry (4,5). Since it appears twice, we know that the dimension of the eigenspace (i.e. for the eigenvalue 1 is equal to 2. Therefore, 