6.2 Eigenvalues Let x be an eigenvector of the matrix A. Then there must exist an eigenvalue λ such that Ax = λx or, equivalently, Ax - λx = 0or (A –
{"Image DocumentName": "6.2 EigenvaluesLet x be an eigenvector of the matrix A. Then there must exist an eigenvalue \u03bb such that Ax = \u03bbx or, equivalently,", "Image ImageDescription": "Ax - \u03bbx = 0 or. (A \u2013 \u03bbI)x = 0. If we define a new matrix B = A \u2013 \u03bbI, then. Bx = 0. If B has an inverse then x = B-10 = 0. But an eigenvector cannot be zero. Thus, it follows that x will be an eigenvector of A if and only if B does not have an inverse, or equivalently det(B)=0, or. det(A \u2013 \u03bbI) = 0. This is called the characteristic equation of A. Its roots determine the eigenvalues of A.", "Image XResolution": "37", "Image YResolution": "37", "Image ResolutionUnit": "Pixels/Centimeter", "Image Software": "SlidePlayer", "Image YCbCrPositioning": "Centered"}