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HP HP-15C User Manual
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Section 12: C
alculating
with Matrices
155
For
÷
,
the
matrix
specifi
ed
in
the
X-re
gister
is
repl
aced
by
its
LU
decomposition.
The
÷
function
calc
ulates
X
îš±
1
Y
usi
ng
a
more
direct
method
than
does
∕
and
*
,
giving
the
result
faster
and
w
i
th
improved
accuracy.
Example:
Using
matrices
A
and
B
from
t
he
pr
evious
exa
mple,
calculate
C
=
A
T
B
.














17
9
7
5
3
1
9
5
4
3
2
1
an
d
B
A
Keystrokes
Display
l>
A
A
2
3
Recalls descriptor
for matrix
A
.
l>
B
b
2
3
Recalls descripto
r for matrix
B
into X-register,
moving matrix
A
descripto
r into Y-register.
´<
C
b
2
3
Designates
m
atr
ix
C
as r
esult
matrix.
´>
5
C
3
3
Calculates
A
T
B
and stores
result in matrix
C
,
which is
redimensioned to 3
×
3.
The result,
m
atrix C, is











168
90
66
95
51
37
73
39
29
C
.
154
156
Table of Contents
Default Chapter
4
Table of Contents
4
The HP-15C: a Problem Solver
12
A Quick Look at V
12
Manual Solutions
13
Programmed Solutions
14
Part I: HP-15C Fundamentals
17
Section 1: Getting Started
18
Power on and off
18
Keyboard Operation
18
Primary and Alternate Functions
18
Prefix Keys
19
Changing Signs
19
Keying in Exponents
19
The "CLEAR" Keys
20
Display Clearing: ` and
21
Calculations
22
One-Number Functions
22
Two-Number Functions and
22
Section 2: Numeric Functions
24
Number Alteration Functions
24
One-Number Functions
25
General Functions
25
Time and Angle Conversions
26
Trigonometric Operations
26
Degrees/Radians Conversions
27
Hyperbolic Functions
28
Logarithmic Functions
28
Two-Number Functions
29
Percentages
29
The Power Function
29
Polar and Rectangular Coordinate Conversions
30
Section 3: the Automatic Memory Stack, LAST X, and Data Storage
32
The Automatic Memory Stack and Stack Manipulation
32
Stack Manipulation Functions
33
The LAST X Register and K
35
Calculator Functions and the Stack
36
Order of Entry and the V Key
37
Nested Calculations
38
Arithmetic Calculations with Constants
39
Storage Register Operations
42
Storing and Recalling Numbers
42
Clearing Data Storage Registers
43
Storage and Recall Arithmetic
43
Overflow and Underflow
45
Problems
45
Section 4: Statistics Functions
47
Probability Calculations
47
Random Number Generator
48
Accumulating Statistics
49
Correcting Accumulated Statistics
52
Mean
53
Standard Deviation
53
Linear Regression
54
Linear Estimation and Correlation Coefficient
55
Other Applications
57
Section 5: the Display and Continuous Memory
58
Display Control
58
Fixed Decimal Display
58
Scientific Notation Display
59
Engineering Notation Display
59
Mantissa Display
60
Round-Off Error
60
Special Displays
60
Annunciators
60
Digit Separators
61
Error Display
61
Overflow and Underflow
61
Low-Power Indication
62
Continuous Memory
62
Status
62
Resetting Continuous Memory
63
Part II: HP-15C Programming
65
Section 6: Programming Basics
66
The Mechanics
66
Creating a Program
66
Loading a Program
66
Intermediate Program Stops
68
Running a Program
68
How to Enter Data
69
Program Memory
70
Further Information
74
Instruction Coding
74
Program Instructions
74
Memory Configuration
75
Program Boundaries
77
Abbreviated Key Sequences
78
Unexpected Program Stops
78
Polynomial Expressions and Horner's Method
79
User Mode
79
Nonprogrammable Functions
80
Problems
81
Section 7: Program Editing
82
The Mechanics
82
Moving to a Line in Program Memory
82
Deleting Program Lines
83
Inserting Program Lines
83
Examples
83
Further Information
85
Single-Step Operations
85
Line Position
86
Initializing Calculator Status
87
Insertions and Deletions
87
Problems
87
Section 8: Program Branching and Controls
90
The Mechanics
90
Branching
90
Conditional Tests
91
Flags
92
Examples
93
Example: Branching and Looping
93
Example: Flags
95
Further Information
97
Goto
97
Conditional Branching
98
Flags
98
Looping
98
The System Flags: Flags 8 and 9
99
Section 9: Subroutines
101
The Mechanics
101
Goto Subroutine and Return
101
Examples
102
Subroutine Limits
102
Further Information
105
Nested Subroutines
105
The Subroutine Return
105
Section 10: the Index Register and Loop Control
106
The V and % Keys
106
Direct Versus Indirect Data Storage with the Index Register
106
The Index Register
106
Indirect Program Control with the Index Register
107
Program Loop Control
107
The Mechanics
107
Index Register Storage and Recall
107
Exchanging the X-Register
108
Index Register Arithmetic
108
Indirect Branching with
108
Indirect Display Format Control with V
109
Indirect Flag Control with
109
Loop Control with Counters: I and E
109
Examples
111
Examples: Register Operations
111
Example: Loop Control with S
112
Example: Display Format Control
114
Further Information
115
Index Register Contents
115
I and E
116
Indirect Display Control
116
Part III: HP-15C Advanced Functions
119
Section 11: Calculating with Complex Numbers
120
The Complex Stack and Complex Mode
120
Creating the Complex Stack
120
Deactivating Complex Mode
121
Complex Numbers and the Stack
121
Entering Complex Numbers
121
Changing Signs
124
Manipulating the Real and Imaginary Stacks
124
Stack Lift in Complex Mode
124
Clearing a Complex Number
125
Entering a Real Number
128
Entering a Pure Imaginary Number
129
Storing and Recalling Complex Numbers
130
Operations with Complex Numbers
130
One-Number Functions
131
Stack Manipulation Functions
131
Two-Number Functions
131
Conditional Tests
132
Complex Results from Real Numbers
133
Polar and Rectangular Coordinate Conversions
133
Problems
135
For Further Information
137
Section 12: Calculating with Matrices
138
Matrix Dimensions
140
Dimensioning a Matrix
141
Changing Matrix Dimensions
142
Displaying Matrix Dimensions
142
Storing and Recalling Matrix Elements
143
Storing and Recalling All Elements in Order
143
Checking and Changing Matrix Elements Individually
145
Storing a Number in All Elements of a Matrix
147
Matrix Operations
147
Matrix Descriptors
147
The Result Matrix
148
Copying a Matrix
149
One-Matrix Operations
149
Scalar Operations
151
Arithmetic Operations
153
Matrix Multiplication
154
Solving the Equation AX = B
156
Calculating the Residual
159
Using Matrices in LU Form
160
Calculations with Complex Matrices
160
Storing the Elements of a Complex Matrix
161
And Z
164
The Complex Transformations between Z
164
Inverting a Complex Matrix
165
Multiplying Complex Matrices
166
Solving the Complex Equation AX = B
168
Miscellaneous Operations Involving Matrices
173
Using a Matrix Element with Register Operations
173
Using Matrix Descriptors in the Index Register
173
Conditional Tests on Matrix Descriptors
174
Stack Operation for Matrix Calculations
174
Using Matrix Operations in a Program
176
Summary of Matrix Functions
177
For Further Information
179
Section 13: Finding the Roots of an Equation
180
Using
180
When no Root Is Found
186
Choosing Initial Estimates
188
Using _ in a Program
192
Restriction on the Use of
193
Memory Requirements
193
For Further Information
193
Section 14: Numerical Integration
194
Using F
194
Accuracy of F
200
Using F in a Program
203
Memory Requirements
204
For Further Information
204
Appendix A: Error Conditions
205
Appendix B: Stack Lift and the LAST X Register
209
Digit Entry Termination
209
Stack Lift
209
Disabling Operations
210
Enabling Operations
210
Neutral Operations
211
LAST X Register
212
Appendix C Memory Allocation
213
The Memory Space
213
Registers
213
Memory Reallocation
215
Memory Status (W)
215
The M % Function
215
Restrictions on Reallocation
216
Program Memory
217
Automatic Program Memory Reallocation
217
Two-Byte Program Instructions
218
Memory Requirements for the Advanced Functions
218
Appendix D: a Detailed Look at
220
How
220
Accuracy of the Root
222
Interpreting Results
226
Finding Several Roots
233
Limiting the Estimation Time
238
Counting Iterations
239
For Advanced Information
239
Specifying a Tolerance
239
Appendix E: a Detailed Look at F
240
How F Works
240
Accuracy, Uncertainty, and Calculation Time
241
Uncertainty and the Display Format
245
Conditions that Could Cause Incorrect Results
249
Conditions that Prolong Calculation Time
254
Obtaining the Current Approximation to an Integral
257
For Advanced Information
258
Appendix F: Batteries
259
Low-Power Indication
259
Installing New Batteries
259
Verifying Proper Operation (Self-Tests)
261
Function Summary and Index
262
Complex Functions
262
Conversions
262
Digit Entry
262
Display Control
263
Hyperbolic Functions
263
Index Register Control
263
Logarithmic and Exponential Functions
263
Mathematics
264
Matrix Functions
264
Number Alteration
265
Percentage
266
Prefix Keys
266
Probability
266
Stack Manipulation
266
Statistics
267
Storage
267
Trigonometry
268
Programming Summary and Index
269
Subject Index
271
Canadian Notice
285
Avis Canadien
285
European Union Regulatory Notice
286
Japanese Notice
287
Other manuals for HP HP-15C
Advanced Functions Handbook
224 pages
4
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HP HP-15C Specifications
General
Brand
HP
Model
HP-15C
Category
Calculator
Language
English
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