What you're looking for is not called the "characteristics equation", but the characteristic polynomial.
More test cases, please. ;-)
Test for balanced parentheses
Replicate elements in vectors
Return 'on' or 'off'
Upper triangular matrix
Find the mode of the given input
Convert number from given base to other base
Do operation as per given string
Add two hex numbers
Check that number is whole number
Find 10's complement
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