HP 15c Scientific manual Inverting a Complex Matrix

Section 12: Calculating with Matrices 165

Inverting a Complex Matrix

You can calculate the inverse of a complex matrix by using the fact that ( )-1= ( -1).

To calculate inverse, Z-1, of a complex matrix Z:

1.Store the elements of Z in memory, in the form either of ZP or of ZC

2.Recall the descriptor of the matrix representing Z into the display.

3.If the elements of Z were entered in the form ZC, press ´p to transform ZC into ZP

4.	Press ´>2 to transform ZP into .
5.	Designate a matrix as the result matrix. It may be the same as the
	matrix in which is stored.

6.Press ∕. This calculates ( )-1, which is equal to ( -1). The values of these matrix elements are stored in the result matrix, and the descriptor of the result matrix is placed in the X-register.

7.Press ´>3 to transform ( -1) into (Z-1)P.

8.If you want the inverse in the form (Z-1)C, press c

You can derive the complex elements of Z-1by recalling the elements of ZP or ZC and then combining them as described earlier.

Example: Calculate the inverse of the complex matrix Z from the previous example.

⎡4		7⎤
⎢		⎥
A = ZP = ⎢	1	3⎥ .
⎢	3	− 2⎥
⎢		⎥
⎣⎢5		8⎦⎥

Keystrokes	Display
l>A A		4	2	Recalls descriptor of matrix A.
´>2	A	4	4	Transforms ZP into and
				redimensions matrix A.