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THE EIGENVALUE PROBLEM Let A be an n n square matrix. If there is a number
 

Summary: THE EIGENVALUE PROBLEM
Let A be an n n square matrix. If there is a number
and a column vector v 6= 0 for which
Av = v
then we say is an eigenvalue of A and v is an associated
eigenvector. Note that if v is an eigenvector, then any
nonzero multiple of v is also an eigenvector for the same
eigenvalue .
Example: Let
A =
"
1:25 0:75
0:75 1:25
#
(1)
The eigenvalue-eigenvector pairs for A are
1 = 2; v(1) =
"
1
1

  

Source: Atkinson, Kendall - Departments of Computer Science & Mathematics, University of Iowa

 

Collections: Computer Technologies and Information Sciences