A(3*3) real matrix has an eigenvalue i, then its other two eigenvalues can be? a)0,1 b)-1,i c)2i,-2i d)0,-2i
Answer (1)
13th Jul, 2020
The sum of all the eigenvalues of a matrix is equal to the trace of the matrix. And since the matrix is real, the trace should also be a real value. Which further implies that the sum of all the eigenvalues should be a real number. So, add all the three eigenvalues and check which option is giving the sum a real number. So, checking all the options, you get that no option can be correct answer. However, if you do option b as (1, -i) then it can be the correct answer.
Hope this helps.
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