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How can I prove that if two polynomials (of matrix coefficients) agree in a neighborhood of $0$, then they are identical?

Thank you!

  • 0
    So these are polynomials in $M_n(\mathbb C)[X]$ treated as functions on $M_n(\mathbb C)$?2012-05-07
  • 0
    Yes, that's exactly the form of polynomials I am talking about.2012-05-07
  • 0
    This is mildly overkill, but it follows from the combinatorial Nullstellensatz (http://www.math.tau.ac.il/~nogaa/PDFS/null2.pdf).2012-05-07
  • 1
    All derivatives of the difference are zero in a nbh. of $0$.2012-05-07

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