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MATH 17100
28446
11/23/2009
Eigenvalues and eigenvectors of a Matrix
Given a
square
matrix
A
, and a vector
x
, the product
Ax
is also a vector, which, in general, has
a magnitude and direction different from
x
. In other words, the square matrix
A
transforms
vectors to vectors which, in general, have different orientations.
We ask: Given the
nn
matrix
A
, are there certain preferred or
characteristic directions
along
which vectors get transformed without change in orientation?
In other words, given
A
, find
v
such that
Av
v
Vectors oriented along these directions will be transformed into vectors oriented along the same
direction with at most a change in magnitude and sign, these vectors,
v
, are called
eigenvectors
of A, and the scalar
is called the
eigenvalue
associated with the eigenvector
v
.
Finding the characteristic directions with the associated scalar multiples for a given square
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This note was uploaded on 11/04/2010 for the course MATH 17100 taught by Professor Kitchens during the Spring '10 term at IUPUI.
 Spring '10
 KITCHENS
 Eigenvectors, Vectors

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