(l) = |A −lI| = 0 are called characteristic roots,
latent roots, eigenvalues or proper values of the
matrix A.
1. If A is real then the eigenvalues will be real
or complex conjugate pairs.
Let l
1
, l
2
,
…,
l
n
be the eigenvalues of A
i.e., the roots of the characteristic polynomial
P
n
(l). Then
P
n
(l) = (l
1
− l) (l
2
− l)
…
(l
n
− l)
= (−1)
n
(l − l
1
) (l − l
2
)
…
(l − l
n
)
= (−1)
n
[l
n
+ (−1) (l
1
+ l
2
+
…
+ l
n
) l
n−1
+
…
+ (−1)
n
l
1
⋅l
2
…
l
n
]
2. The sum of the eigenvalues of a matrix is
the sum of the elements of the principal
diagonal.
3. The product of the eigenvalues ...
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