hi. i have recently become very interested in the idea of the nth roots of unity. i have discovered how to calculate them (using eigenvalues), and i find it very fascinating that there are not n many nth roots of unity(unlike scalars).(adsbygoogle = window.adsbygoogle || []).push({});

aparently in the case where the matrix is 2x2, there are n^2 roots of unity

my questions:

given a size=k matrix, find the nth roots of unity. how many roots of unity are there? i want a general formula. is it n^k?

What is the geometrical interperetation of the nth roots of unity of a matrix? the determinants of the nth roots are equal(analogous to the fact that the nth roots of unity of a scalar are points on a circle), but what about the placement of the vectors that compose the matrix? in other words, what is analogous to the fact that the roots of unity of a scalar form a regular polygon?

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# Roots of unity of matrices

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