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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
3-8 Mathematical Methods
For i = j,
a
ii
= a
ii
a
ii
a
ii
= 0 I
m
(a
ii
) = 0.
This implies that the main diagonal elements of a
Hermitian matrix are purely real or zero.
E.g.
11 23
243
, 1 0 2 .
43 6
23 2 5
ii
i
ii
i
ii
+−
⎡⎤
⎢⎥
⎡⎤
−−
⎢⎥
⎢⎥
+
⎣⎦
⎢⎥
++
⎣⎦
are Her
mitian matrices.
3.4.6 Skew-Hermitian Matrix
A square matrix A = [a
ij
] is called a skew- Hermitian
matrix if
a
ji
= a
ij
for all i, j. i.e., A
q
= A. For
i = j,
a
ii
= – a
ii
a
ii
+
a
ii
= 0 R
e
(a
ii
) = 0.
This implies that the main diagonal elements of a
skew-Hermitian matrix are purely imaginary or zero.
E.g.
00
21
, 0 0
10
00
i
ii
i
i
i
⎡⎤
−+
⎡⎤
⎢⎥
⎢⎥
⎢⎥
+
⎣⎦
⎢⎥
⎣⎦
are skew-Hermitian matrices.
3.4.7 Unitary Matrix
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Publisher Resources

ISBN: 9781299446557Publisher Website