Geodesic
A note on Brauer's theorem
The Teaching of Mathematics, XXIII (2020) no. 1, p. 17
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We present an elementary proof of Brauer's theorem, which shows how knowledge of an eigenpair can be used to change a single eigenvalue of a matrix.
Classification : 97H60, 15A18, H65
Keywords: eigenvalue, eigenvector, rank-one modification, Brauer. 
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Aaron Melman. A note on Brauer's theorem. The Teaching of Mathematics, XXIII (2020) no. 1, p. 17 . http://geodesic.mathdoc.fr/item/TM2_2020_XXIII_1_a1/