May I ask what is the definition of Nilpotent matrix. I suppose that is A^k =0 for some k? If I am right, then 0 must be an eigenvalue of A, then there is some issues for the test problems.
@Ling Liang , take some tolerance while checking the equality of eigen value with zero.
Back to basics 17 - white space
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Try 1.5.4: Celsius to Fahrenheit
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