HP 15c Scientific The Complex Transformations Between ZP and Z

164 Section 12: Calculating with Matrices

Matrix A now represents the complex matrix Z in ZP form:

⎡4		7⎤	}Real P art
⎢	1	⎥
A = ZP = ⎢		3⎥.
⎢	3	− 2⎥	Imaginary P art
⎢		⎥
⎣⎢5		8⎦⎥	}

The Complex Transformations Between ZP and Z

An additional transformation must be done when you want to calculate the product of two complex matrices, and still another when you want to calculate the inverse of a complex matrix. These transformations convert between the ZP representation of an m×n complex matrix and a 2m×2n partitioned matrix of the following form:

⎡X −Y⎤
Z = ⎢	⎥ .
⎣Y	X⎦

The matrix created by the > 2 transformation has twice as many elements as ZP.

For example, the matrices below show how is related to ZP.

⎡	1 −6⎤	~	⎡	1 −6	4 −5⎤
ZP = ⎢	⎥	↔ Z = ⎢			⎥
⎣− 4 5⎦			⎣− 4 5		1 − 6⎦

The transformations that convert the representation of a complex matrix between ZP and are shown in the following table.

Pressing	Transforms	Into
´>2	ZP
´>3		ZP

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