162 Section 12: Calculating with Matrices
then Z can be represented in the calculator by
A = Z
P
=
X
Y
=
x
11
x
12
x
21
x
22
y
11
y
12
y
21
y
22
.
Suppose you need to do a calculation with a complex matrix that is not
written as the sum of a real matrix and an imaginary matrix—as was the
matrix Z in the example above—but rather written with an entire complex
number in each element, such as
Z =
x
11
+iy
11
x
12
+iy
12
x
21
+iy
21
x
22
+iy
22
.
This matrix can be represented in the calculator by a real matrix that looks
very similar—one that is derived simply by ignoring the i and the + sign.
The 2 × 2 matrix Z shown above, for example, can be represented in the
calculator in “complex” form by the 2 × 4 matrix.
A = Z
C
=
x
11
y
11
x
12
y
12
x
21
y
21
x
22
y
22
.
The superscript C signifies that the complex matrix is represented in a
“complex-like” form.
Although a complex matrix can be initially represented in the calculator
by a matrix of the form shown for Z
C
, the transformations used for
multiplying and inverting a complex matrix presume that the matrix is
represented by a matrix of the form shown for Z
P
. The HP 15c provides
two transformations that convert the representation of a complex matrix
between Z
C
and Z
P
:
Pressing Transforms Into
´ p
Z
C
Z
P
| c
Z
P
Z
C
To do either of these transformations, recall the descriptor of Z
C
or Z
P
into
the display, then press the keys shown above. The transformation is done
to the specified matrix; the result matrix is not affected.
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