HP 15c Scientific manual Storing the Elements of a Complex Matrix

Section 12: Calculating with Matrices 161

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:

⎡X⎤ }		Real Part
ZP = ⎢ ⎥	}	Imaginary P art
⎣Y⎦

The superscript P signifies that the complex matrix is represented by a partitioned matrix.

All of the elements of ZP are real numbers – those in the upper half 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 ZP 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

⎡ x	x	⎤	and	⎡ y	y	⎤	,
X = ⎢ 11	12	⎥		Y = ⎢ 11	12	⎥
⎣x21	x22	⎦		⎣ y21	y22	⎦

then Z can be represented in the calculator by

			⎡ x11		x12		⎤
⎡X⎤			⎢ x		x		⎥
A = Z P = ⎢	Y	⎥	= ⎢	21		22	⎥ .
⎣		⎦	⎢ y		y		⎥
			⎢	11		12	⎥
					y
			⎢ y	21		22	⎥
			⎣				⎦