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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
2-2 Mathematical Methods
2.3.3 Procedure for Finding
Eigenvalues and
Eigenvectors
1. Solve the characteristic equation P(l) =
det(A lI) = 0 for eigenvalues l
i
. If A is an
n-square matrix then the eigenvalues will
be n; repeated roots being counted accord-
ing to their multiplicity.
2. Substituting a specific value l
i
solve the
system of linear homogeneous equations
(A l I )X = 0 to obtain the corresponding
eigenvector X
i
.
Orthogonal matrix: A real square matrix A is called
an orthogonal matrix if A
T
A = I = AA
T
or equiva-
lently A
T
= A
1
.
Since 1 = |I| = |A
T
| = |A
T
||A| = |A|
2
, |A| = ±1.
A is nonsingular and A
1
exists. The linear ...
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Publisher Resources

ISBN: 9781299446557Publisher Website