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Chapter 5
Matrices and linear algebra
The HP 49G has extensive capabilities for entering and manipulating
anrays. An array object can be a vector or matrix.
Many of the matrix operations described in this chapter also apply to
vectors. Wherever this is the case, the more general term array is used
instead of m ati'ix.
By default, Matrix Writer will interpret a one-row array as a vector rather
than as a matrix. If you want a one-row array interpreted as an array, press
VEC first.
For instructions on how to create an ainay—and how to open an array in
Matrix Writer—see chapter 8 of the User’s Guide.
Matrix Writer operations
The following summarizes the operations that are available in Matrix
Writer.
To move around an array
Method 1: using arrow keys
Press the aiTow keys to move the cursor from cell to cell.
You can press 0 before an arrow key to move the cursor directly to an
outermost row or column:
• 0® moves the cursor to the last column
•
0
® moves the cursor to the first row
• © @ moves the cursor to the first column
• © @ moves the cursor to the last row.
Matrices and Linear algebra Page 5-1
- ADVANCED 4
- USER’S GUIDE 4
- Contents 6
- Chapter 4: The Stack 4-1 7
- Chapter 8: Number bases 8-1 8
- Chapter 11: Memory 11-1 10
- Index 1-1 11
- Material covered 12
- The HP 49G documentation set 13
- Chapter 1 14
- Entering commands 14
- Keyboard entry 14
- Subject-specific menus 14
- Sub-menus 15
- (ENTER) 16
- Scrolling through the catalog 17
- (ALPHA) 18
- (ALPHA)© 18
- Typing commands 19
- Chapter 2 20
- System Flags 20
- Displaying system Flags 20
- Setting and clearing Flags 21
- Method 3 22
- Flag commands 23
- User Flags 23
- Chapter 3 24
- Command line operations 24
- Activating the command line 24
- Positioning the cursor 25
- Page 3-3 26
- Selecting characters 27
- Copy, cut, and paste 27
- Editing the command Line 28
- Inserting characters 29
- Editing complex objects 29
- Suspending editing 30
- Find and replace 31
- Find next 32
- OK or (ENTER) 33
- Command Line operations 34
- Page 3-11 34
- Command Line information 35
- ® (0) for BOLD 36
- Chapter 4 38
- The Stack 38
- Using the stack 38
- Example stack calculations 39
- Method 1 40
- Method 2 40
- Multi-command calculations 41
- Chapter 5 42
- Matrices and linear algebra 42
- Matrix Writer operations 42
- Method 2: the GOTO command 43
- To edit an array 43
- Page 5-3 44
- Manipulating columns and rows 45
- To delete a row 46
- Key Description 47
- To create an identity matrix 48
- Assembling matrices 49
- 0 (PRG) TYPE ^ARRY 50
- Disassembling matrices 51
- Inserting rows and columns 52
- To swap two rows in an array 53
- Characterizing matrices 55
- Page 5-15 56
- To transpose a matrix 57
- To invert a square matrix 57
- More matrix arithmetic 58
- TransForming complex matrices 59
- Linear algebra topics 60
- 0 (iliCES) EIGENVECTOR EGV 61
- FACTORIZATION SVL 61
- FACTORIZATION LU 62
- FACTORIZATION LO 62
- FACTORIZATION OR 62
- FACTORIZATION 62
- FACTORIZATION SVD 63
- Chapter 6 64
- Unit objects 64
- Unit prefixes 66
- Converting units 67
- Calculating with units 68
- Sample unit calculations 69
- Powers. To cube 2ft/s 70
- Factoring unit expressions 71
- Converting temperature units 72
- 0 iOirS] TOOLS CONVERT 73
- Chapter 7 74
- Constants Library 74
- 02 dielectric constant 75
- To view the constants library 76
- Page 7-4 77
- Constants library 77
- Chapter 8 78
- Number bases 78
- To set the wordsize 79
- To enter a binary integer 79
- Binary integer arithmetic 80
- Using Boolean operators 82
- Manipulating bits and bytes 83
- Chapter 9 84
- Lists and Sequences 84
- Creating Lists 84
- List Processing 85
- 3. Press (ENTER) 86
- (ME) LIST ADD 86
- 4. Press (ENTER) 86
- To concatenate two lists 87
- Page 9-5 88
- DOSUB command 89
- 0 ® LIST PROCEDURES STREAM 89
- List Manipulations 90
- (00 LIST ELEMENTS PUTÌ 90
- (00 LIST ELEMENTS SIZE 90
- 0 (flGlLIST ELEMENTS POS 91
- 0 (PEG) LIST 91
- 0 {® LIST SUB 91
- 0 ® LIST REEL 91
- Sequences 92
- 0 (MDi) LIST Slist 93
- 0 O LIST PLIST 93
- 0 (MTH) LIST Dlist 93
- Chapter 10 94
- Page 10-2 95
- Examples 96
- To keep the same scaling: 97
- PDM((-6,-6), (6,9)) 98
- PDM(#105h, #3Fh) 98
- Press (N0 CALC 98
- Saving and Restoring Plots 99
- Advanced plotting options 100
- Page 10-7 100
- 0 O, type VPAR and press 101
- Chapter 11 102
- How memory is structured 102
- Accessing port contents 103
- Backup objects 103
- Backing up and restoring HOME 104
- Using data in backup objects 105
- Page 11-5 106
- Library objects 107
- How the HP 49G manages memory 108
- Ins. Mem. Need x bytes 109
- Chapter 12 110
- Date and time arithmetic 110
- Date and time Formats 110
- Date and time tools 111
- (£ED DATE+ 112
- Calculating with times 113
- (CAT) HMS^ 114
- System time 115
- TOOLS TICKS 116
- 0 TOOLS TICKS 116
- STACK SWAP and continue with 116
- Chapter 13 118
- Customization 118
- Creating menus 118
- User mode 119
- Assigning user keys 120
- To unassign a user key 121
- Disabling keys in user mode 121
- To enable disabled keys 122
- Chapter 14 124
- Computer Algebra Commands 124
- Page 14-2 125
- Arithmetic Integer commands 126
- Arithmetic Polynomial 126
- Arithmetic Modulo commands 126
- Calculus commands 127
- Exp and Lin commands 127
- Matrix-related commands 127
- Symbolic solve commands 127
- Trigonometry commands 128
- Alphabetical command list 129
- AC0S2S(ACOS(2/3)+ACOS(X)) 130
- ADDTMOD (X-^2 + 3*X+6,9*X+3) 130
- X''2-2*X+2 130
- I ~x" 131
- {{1,0},{0,1}} 132
- Page 14-10 133
- 0{M£) DERIV AND INTEG 134
- 2 "I T 135
- 1- 2>’(x) = 136
- RKASTH) modulo 137
- X + 3x + 2 138
- (3&S) LIMITS & SERIES 139
- POLYNOMIAL 140
- EGCD(X^2+1,X-1) 140
- {2,1,-{X+D } 140
- EXLR(SIN(X)=5*X+Y) 141
- {SIN(X) 5*X+Y] 141
- EXPAN((X^2+2*X+1)/(X+1)) 142
- EXPANDMOD 143
- FACTORMOD 144
- 0(mTh) polynomial 145
- R(ARiTH) POLYNOMIAI 146
- FXND((X-3)^2/(Z+4)) 147
- {[l,-A-2] [[1,A][0,1]], 148
- GCD(2805,99) 148
- HADAMARD 149
- R(MTH) POLYNOMIAL 150
- HERMITE(4) 150
- 0@£) DERIV & INTEG 150
- RQiMTRICES] 151
- + bv = c 152
- IBERNOULLI 153
- ICHINREM 154
- IDIV2(11632,864) 155
- {13,400} 155
- ILAP{1/(X-5)^2) 156
- X*EXP(5*X) 156
- . & integ 157
- INTVX (X"'2*LN(X) ) 157
- INVMOD(2) 157
- IREMAINDER 158
- ISPRIME? 158
- LAGRANGE 159
- LAGRANGE {'342 160
- LEGENDRE 162
- LIMITS&SERIES 163
- LINSOLVE 164
- LNCOLLECT 165
- R (R1ces)operations 166
- NEXTPRIME 167
- PARTFRAC 168
- Q@IH) polynomial 168
- PREVPRIME 170
- PROPFRAC 171
- ^(Inr(z)) 172
- + X}’ + V 173
- ] , [X,Y]} 173
- REMAINDER 174
- RESULTANT 175
- RISCH(Y''3-3*Y+2,Y) 176
- LINEAR SYSTEMS 176
- systems 176
- 0{M£) LIMITS & SERIES 177
- {X+3,X-3} 179
- SINCOS(EXP(i*X)) 180
- COS(X)+iSIN(X) 180
- SOLVE(X"3-X-9,X) 180
- {X=2.24004098747} 180
- Result: {X=2.2400} 181
- SYLVESTER 182
- TABVAL(X^2+l,{1 2 3}) 183
- {{1 2 3},{2 5 10} } 183
- TCHEBYCHEFF 185
- TCOLLECT 185
- TEXPAND (LN( SIN (X-FY) ) ) 186
- TLIN(COS(X)"4) 186
- H (MATRICES) OPERATIONS 187
- (LN(X+i)) 187
- (sinx) +(cosx) = 1 188
- Page 14-66 189
- VANDERMONDE 190
- XNUM{ {TC/2,3*e, 4*C0S (2} ) 191
- 1.66458734619} 191
- XQ(.3658) 191
- 1829/5000 191
- Page 14-69 192
- Page 1-1 194
- Page 1-2 195
- Page 1-3 196
- Page 1-4 197
- HEWLETT' 199
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