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How does the sum of a matrix's eigenvalues relate to the matrix itself?

  • A.it equals the sum of all the entries
  • B.it equals the trace
  • C.it equals the determinant
  • D.it equals the rank

Answer: B

Both quantities are the coefficient of the second-highest power in the characteristic polynomial, up to sign. It gives a quick arithmetic check on any set of computed eigenvalues, alongside the corresponding product relation.

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