Search results

  • * [[Polynomials]] ** [[Elementary symmetric polynomial]]
    2 KB (198 words) - 15:06, 7 December 2024
  • where <math>S_n</math> denotes the <math>n</math>-th [[elementary symmetric sum]]. [[Category:Polynomials]]
    4 KB (704 words) - 07:28, 24 November 2024
  • ...be expressed as linear combinations of real numbers times the [[elementary symmetric polynomial]]s in <math>x_1, \dotsc, x_n</math>; thus they are real numbers. [[Category:Polynomials]]
    5 KB (832 words) - 13:22, 11 January 2024
  • ...t states that the [[elementary symmetric polynomial | elementary symmetric polynomials]] of its roots can be easily expressed as a ratio between two of the polyno ...th>, and let <math>s_j</math> be the <math>j^{\text{th}}</math> elementary symmetric polynomial of the roots.
    3 KB (528 words) - 20:24, 21 October 2024
  • The generalization to characteristic polynomials with multiple roots is not difficult from here, and is left to the reader. ...<math>f = gh</math>, where <math>g</math> and <math>h</math> are non-zero polynomials such that <math>\text{gcd}\,(g,h) = 1</math>, and such that <math>f(A) = O<
    19 KB (3,412 words) - 13:57, 21 September 2022