162 Section 12: Calculating with Matrices

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

x

+ iy

x

+ iy

Z = 11

11

12

12

.

x21

+ iy21

x22

+ iy22

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

y

 

x

y

 

= 11

 

11

12

 

12

.

 

x21

y21

x22

y22

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 ZC, the transformations used for multiplying and inverting a complex matrix presume that the matrix is represented by a matrix of the form shown for ZP. The HP-15C provides two transformations that convert the representation of a complex matrix between ZC and ZP:

Pressing

Transforms

Into

 

 

 

´p

ZC

ZP

c

ZP

ZC

To do either of these transformations, recall the descriptor of ZC or ZP into the display, then press the keys shown above. The transformation is done to the specified matrix; the result matrix is not affected.