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Instead, calculations with complex matrices are performed by using real
matrices derived from the original complex matrices – in a manner to be
described below – and performing certain transformations in addition to the
regular matrix operations. These transformations are performed by four
calculator functions. This section will describe how to do these calculations.
(There are more examples of calculations with complex matrices in the
HP-15C Advanced Functions Handbook.)
Storing the Elements of a Complex Matrix
Consider an m×n complex matrix Z = X + iY, where X and Y are real
m×n matrices. This matrix can be represented in the calculator as a
2m×n ―partitioned‖ matrix:
The superscript P signifies that the complex matrix is represented by a
partitioned matrix.
All of the elements of Z
represent the elements of the real part (matrix X), those in the lower half
represent the elements of the imaginary part (matrix Y). The elements of Z
are stored in one of the five matrices (A, for example) in the usual manner,
as described earlier in this section.
For example, if Z = X + iY, where
then Z can be represented in the calculator by
Section 12: Calculating with Matrices
X
}
P
Z
Y
}
P
are real numbers – those in the upper half
x
x
11
12
X
and
x
x
21
22
X
P
A
Z
Y
Real
Part
Imaginary
Part
y
y
11
12
Y
y
y
21
22
x
x
11
12
x
x
21
22
.
y
y
11
12
y
y
21
22
,
161
P
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