HP 15c Collector's Edition User Manual

162 Section 12: Calculating with Matrices
then Z can be represented in the calculator by
A = Z
P
=


X
Y


= 







x
11
x
12
x
21
x
22
y
11
y
12
y
21
y
22







.
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
Z = 
x
11
+iy
11
x
12
+iy
12
x
21
+iy
21
x
22
+iy
22
.
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
11
y
11
x
12
y
12
x
21
y
21
x
22
y
22
.
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 Z
C
, the transformations used for
multiplying and inverting a complex matrix presume that the matrix is
represented by a matrix of the form shown for Z
P
. The HP 15c provides
two transformations that convert the representation of a complex matrix
between Z
C
and Z
P
:
Pressing Transforms Into
´ p Z
C
Z
P
| c Z
P
Z
C
To do either of these transformations, recall the descriptor of Z
C
or Z
P
into
the display, then press the keys shown above. The transformation is done
to the specified matrix; the result matrix is not affected.

HP 15c Collector's Edition Specifications

General

Model	HP 15c Collector's Edition
Category	Calculator
Type	Scientific
Power Source	Battery
Manufacturer	HP
Display	LCD
Functions	complex numbers, matrix operations

Summary

Introduction

This Handbook

Outlines the structure of the manual, detailing its parts and how to use it for learning.

The HP Community

Discusses user groups and websites for HP calculator enthusiasts and information sharing.

Part I: HP 15c Fundamentals

Section 1: Getting Started

Covers basic operations like powering on, keyboard layout, and primary/alternate functions.

Section 2: Numeric Functions

Explains essential numeric operations including logs, trig, powers, and conversions.

Section 3: The Automatic Memory Stack, LAST X, and Data Storage

Details the RPN stack, LAST X register, and data storage operations.

Part II: HP 15c Programming

Section 6: Programming Basics

Introduces core programming concepts: creating, loading, running programs, and memory.

Section 8: Program Branching and Controls

Covers controlling program flow using branching, loops, and conditional tests.

Part III: HP 15c Advanced Functions

Section 11: Calculating With Complex Numbers

Covers entering, manipulating, and performing calculations with complex numbers.

Section 12: Calculating With Matrices

Explains matrix operations, including dimensioning, element access, and calculations.

Section 13: Finding the Roots of an Equation

Details using the SOLVE function for numerical root finding and equation solving.

Section 14: Numerical Integration

Explains how to perform numerical integration using the ∫f(x)dx key and subroutines.

Appendix A: Error Conditions

Error 8: No Root

Explains the error when the SOLVE function cannot find a root.

Error 0: Improper Mathematics Operation

Lists and explains errors related to mathematical operations and illegal arguments.

Appendix D: A Detailed Look at SOLVE

How SOLVE Works

Explains the numerical technique and logic behind the SOLVE algorithm.

Finding Several Roots

Discusses methods for finding multiple roots of an equation using the SOLVE function.