HP 15c Manual

 Section 12: Calculating with Matrices 171 
 
Keystrokes Display 
´> 2 A 4 4 Transforms AP into Ã. 
´< C A 4 4 Designates matrix C as 
result matrix. 
÷ C 4 1 
Calculates XP and stores 
in C. 
|c C 2 2 Transforms XP into XC. 
lC 0.0372   Recalls c11. 
lC 0.1311   Recalls c12. 
lC 0.0437   Recalls c21. 
lC 0.1543   Recalls c22. 
´U 0.1543   Deactivates User mode. 
´> 0 0.1543   Redimensions all matrices 
to 0×0. 
The currents, represented by the complex matrix X, can be derived from C 
 
Solving  the...

172 Section 12: Calculating with Matrices 
 
1. Store the elements of A in memory, in the form either of AP or of 
AC. 
2. Recall the descriptor of the matrix representing A into the display. 
3. If the elements of A were entered in the form AC, press ´ p 
to transform AC into AP. 
4. Press ´> 2 to transform AP into Ã. 
5. Press O< to designate the matrix representing A as the 
result matrix. 
6. Press ∕ to calculate (Ã)-1. 
7. Redimension A to have half the number of rows as indicated in the 
display of...

 Section 12: Calculating with Matrices 173 
 
A problem using this procedure is given in the HP-15C Advanced Functions 
Handbook under Solving a Large System of Complex Equations. 
Miscellaneous Operations Involving Matrices 
Using a Matrix Element With Register Operations 
If  a  letter  key  specifying  a  matrix  is  pressed  after  any of  the  following 
function keys, the operation is performed using the matrix element specified 
by  the  row and column numbers in R0 and R1, just as though  it...

174 Section 12: Calculating with Matrices 
 
 Pressing ´mV dimensions the matrix specified in RI 
according to the dimensions in the X- and Y-registers. 
 Pressing lmV recalls to the X- and Y-registers the 
dimensions of the matrix specified in RI. 
 Pressing GV or tV has the same result as pressing 
G or t followed by the letter of the matrix specified in RI. 
(This is not actually a matrix operation – only the letter in the 
matrix descriptor is used.) 
Conditional Tests on Matrix Descriptors 
Four...

 Section 12: Calculating with Matrices 175 
 
 
Several  matrix  functions  operate  on  the  matrix  specified  in  the  X-register 
only  and  store  the  result  in  the  same  matrix.  For  these  operations  the 
contents  of  the  stack  (including  the LAST  X  register)  are  not  moved – 
although the display changes to show the new dimensions if necessary. 
For  the > 7, > 8,  and > 9  functions,  the  matrix 
descriptor  specified  in  the  X-register  is  placed  in  the  LAST  X  register...

176 Section 12: Calculating with Matrices 
 
 
Using Matrix Operations in a Program 
If  the  calculator  is  in  User  mode  during  program  entry  when  you  enter  a 
O or l{A through E, %}  instruction  to  store  or  recall  a 
matrix  element,  a u replaces  the  dash  usually  displayed  after  the  line 
number.  When  this  line  is  executed  in a  running  program,  it  operates  as 
though  the  calculator  were  in  User  mode.  That  is,  the  row  and  column 
numbers  in R0 and  R1 are...

 Section 12: Calculating with Matrices 177 
 
 
The > 7 (row norm) and > 8 (Frobenius norm) functions also 
operate as conditional branching instructions in a program. If the X-register 
contains a  matrix descriptor, these functions calculate the  norm in the  usual 
manner, and program execution continues with the next program line. If the 
X-register contains a number, program execution skips the next line. In both 
cases,  the  original  contents  of  the  X-register  are  stored  in  the  LAST  X...

178 Section 12: Calculating with Matrices 
 
Keystroke(s) Results 
result matrix. 
´> 6 Calculates residual in result matrix. 
´> 7 Calculates row norm of matrix specified in X-
register. 
´> 8 Calculates Frobenius or Euclidean norm of matrix 
specified in X-register. 
´> 9 Calculates determinant of matrix specified in X-
register, Place LU in result matrix. 
´p Transforms ZC into ZP. 
l{A through 
E, %} 
Recalls value from specified matrix, using row and 
column numbers in R0 and R1. 
l|{A 
through E,...

 Section 12: Calculating with Matrices 179 
 
 
Keystroke(s) Results 
O < Designates matrix specified in X-register as result 
matrix. 
´ U Row and column numbers in R0 and R1 are 
automatically incremented each time O or l 
{A through E, %} is pressed. 
∕ Inverts matrix specified in X-register. Stores in result 
matrix. Use ´ ∕ if User mode is on. 
+, - If matrix descriptors specified in both X- and Y-
registers, adds or subtracts corresponding elements of 
matrices specified. If matrix descriptor...

 
180 
Section 13 
Finding the Roots  
of an Equation 
In many applications you need to solve equations of the form 
f(x)=0.* 
This means finding the values of x that 
satisfy  the  equation.  Each  such  value 
of x is called a root of the equation f(x) 
=  0  and  a zero of  the  function f(x). 
These  roots  (or  zeros)  that  are  real 
numbers  are  called real roots (or  real 
zeros). For many problems the roots of 
an  equation  can  be  determined 
analytically  through  algebraic 
manipulation;...