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Question about eigenvalues

  1. Jan 10, 2010 #1
    Let's say I have a 2x2 matrix,we call it A with the eigenvalues +1 , -1.
    Now I lets define that m=m0*A. (m0 is const).
    Are the eigenvalues become +m0 and -m0?
    If so why?
  2. jcsd
  3. Jan 10, 2010 #2
    Because if [tex]\lambda[/tex] satisfies [tex]det(A-\lambda I)=0[/tex] then [tex]\lambda'=m_{0}\lambda[/tex] satisfies [tex]det(M-\lambda' I)=0[/tex], with [tex]M=\lambda' A[/tex]
    You simply multiply the equation by [tex]m^{2}_{0}[/tex] (and under the determinant it becomes just [tex]m_{0}[/tex])/
    Therefore [tex]m_{0}\lambda[/tex] are eigenvalues of [tex]m_{0}A[/tex].
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