rock_mit182
  • rock_mit182
a) Show that the eigenvalues of the 2 X 2 matrix A = [a,b];[c,d] are the solutions of the quadratic equation A^2 - tr(A)lambda + det A = 0, where tr(A) is the trace of A.
Mathematics
katieb
  • katieb
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rock_mit182
  • rock_mit182
amistre64
  • amistre64
i thought AA was just another matrix ... the trace and det are scalars if memory serves also, refresh my memory on the definition of the trace
amistre64
  • amistre64
sum of the main diag ...

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amistre64
  • amistre64
but then A^2 has me befuddled
Michele_Laino
  • Michele_Laino
hint: we can write the subsequent quadratic equation: \[\det \left( {\begin{array}{*{20}{c}} {a - \lambda }&b \\ c&{d - \lambda } \end{array}} \right) = {\lambda ^2} - \left( {a + d} \right)\lambda + ad - bc\]

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