MATLAB: What does MATLAB mean by [number]^(1/integer) after RootOf( poly)

notationrootof

After computing the eigenvalues of a matrix I notice that some solutions are given in the form RootOf( polynomial ) [number]^(1/integer). Example: RootOf(z^4- 1111*z^3+2222*z^2)[1]^(1/2)
I am aware of the meaning of RootOf and what "^(1/integer)" implies, but…:
1.- I am not sure about why the same "[number]" appears in many solutions (as if I am having repeated eigenvectors) and,
2.- after obtaining the numerical answer of "RootOf(poly)", say "ans"; shall I do "ans^(1/integer)" or "ans^integer" to get the solution?
Any information about the notation would be helpful.
Regards.

Best Answer

The notation
RootOf(z^4- 1111*z^3+2222*z^2)[1]^(1/2)
is intended to be equivalent to
temp1 = roots([1, -1111, 2222, 0, 0]);       %except carried out symbolically
temp2 = temp1(1);                            %select the first root
result = temp2^(1/2);
That is, the [1] indicates the first root is being selected, and the ^(1/2) after all of that indicates the square root should be taken.
If you have found the first root numerically, then you would take the square root of it to finish the expression.
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