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Determinants

Therefore, matrix above is skew symmetric.
A
T∗
A
† A square matrix such that A = A , is called Hermitian. For example,
–
1 1 j 2 1 1 + j 2 1 1 + j 2
T
A = 1 + j 3 j A = 1 – j 3 j – A T* = 1 – j 3 j – = A
2 j – 0 2 j 0 2 j 0

Therefore, matrix above is Hermitian.
A
T∗
A
† A square matrix such that A = – A , is called skew−Hermitian. For example,
j 1 – j 2 j – 1 – j – 2 j – – 1 + j – 2
T
A = – 1 – j 3j j A = 1 – j 3j j A T* = 1 + j – 3j j – = – A
– 2 j 0 2 j 0 2 j – 0

Therefore, matrix above is skew−Hermitian.
A

4.4 Determinants

Let matrix be defined as the square matrix
A

a 11 a 12 a 13 … a 1n
a 21 a 22 a 23 … a 2n
A = a 31 a 32 a 33 … a 3n (4.11)

……… … …
a n1 a n2 a n3 … a nn

then, the determinant of , denoted as detA , is defined as
A
detA = a a a …a nn + a a a …a n1 + a a a …a n2 + … (4.12)
13 24 35
11 22 33
12 23 34
a …a a … a–– …a a – a …a a – …
n1 22 13 n2 23 14 n3 24 15
The determinant of a square matrix of order is referred to as determinant of order .
n
n
Let be a determinant of order , that is,
A
2
a a
A = 11 12 (4.13)
a 21 a 22

Numerical Analysis Using MATLAB® and Excel®, Third Edition 4−9
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