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lecture_31 (dragged) 2 - MA 36600 LECTURE NOTES FRIDAY...

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MA 36600 LECTURE NOTES: FRIDAY, APRIL 10 3 Characteristic Polynomials. We give a simple way to compute eigenvalues of an n × n matrix A . Consider the equation A x = λ x = ( λ I A ) x = 0 . Since this holds for a nonzero vector x , we see that the matrix λ I A must be singular. We found before that an n × n matrix is singular if and only if its determinant is zero. Hence we conclude that λ is an eigenvalue for A if and only if λ is a root of the characteristic polynomial p
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