Let M be an n xn matrix over R given by M = D+u®v" where D is a diagonal matrix over R and u, v are column vectors in R". The eigenvalue equation is given by Mx = (D+u®v)x= Ax. Assume that u;v; # 0. Show that リ=1 0 = 1+ r- *p). k=1

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Let M be an n x n matrix over R given by
M = D+u®v"
where D is a diagonal matrix over R and u, v are column vectors in R". The
eigenvalue equation is given by
Mx = (D+u0 vT)x = Ax.
Assume that u;v; + 0. Show that
Σ
+1= 0
(dr – X)
k=1
Transcribed Image Text:Let M be an n x n matrix over R given by M = D+u®v" where D is a diagonal matrix over R and u, v are column vectors in R". The eigenvalue equation is given by Mx = (D+u0 vT)x = Ax. Assume that u;v; + 0. Show that Σ +1= 0 (dr – X) k=1
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