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Mathematical Methods by Pearson
book

Mathematical Methods by Pearson

by E. Rukmangadachari
May 2024
Intermediate to advanced content levelIntermediate to advanced
437 pages
17h 41m
English
Pearson India
Content preview from Mathematical Methods by Pearson
Eigenvalues and Eigenvectors 2-7
The roots of the characteristic equation
P
n
(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
(ll
1
) (ll
2
)
(ll
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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Publisher Resources

ISBN: 9781299446557Publisher Website