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MAKEMAT, ROWNORM, SCHUR, Reduced-Row Echelon Form. Changes a rectangular

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LU MAKEMAT QR RANK ROWNORM RREF SCHUR SIZE 15-12 LU Decomposition. Factors a square matrix into three matrices: {[[lowertriangular]],[[uppertriangular]],[[permutation]]} The uppertriangular has ones on its diagonal. LU (matrix) Make Matrix. Creates a matrix of dimension rows × columns, using expression to calculate each element. If expression contains the variables I and J, then the calculation for each element substitutes the current row number for I and the current column number for J. MAKEMAT(expression, rows, columns) Example MAKEMAT(0,3,3) returns a 3×3 zero matrix, [[0,0,0],[0,0,0],[0,0,0]]. QR Factorization. Factors an m×n matrix into three matrices: {[[m×m orthogonal]],[[m×n uppertrapezoidal]],[[n×n permutation]]}. QR (matrix) Rank of a rectangular matrix. RANK (matrix) Row Norm. Finds the maximum value (over all rows) for the sums of the absolute values of all elements in a row. ROWNORM (matrix) Reduced-Row Echelon Form. Changes a rectangular matrix to its reduced row-echelon form. RREF (matrix) Schur Decomposition. Factors a square matrix into two matrices. If matrix is real, then the result is {[[orthogonal]],[[upper-quasi triangular]]}. If matrix is complex, then the result is {[[unitary]],[[upper-triangular]]}. SCHUR (matrix) Dimensions of matrix. Returned as a list: {rows,columns}. SIZE (matrix) Matrices

Section	Page
Contents	9
Manual conventions	9
Notice	10
Getting started	11
On/off, cancel operations	11
The display	12
The keyboard	13
Menus	18
Input forms	19
Mode settings	20
Setting a mode	21
Aplets (E-lessons)	22
Aplet library	26
Aplet views	26
Aplet view configuration	28
Mathematical calculations	29
Using fractions	35
Complex numbers	39
Catalogs and editors	40
Aplets and their views	41
Aplet views	41
About the Symbolic view	41
Defining an expression (Symbolic view)	41
Evaluating expressions	43
About the Plot view	45
Setting up the plot (Plot view setup)	45
Exploring the graph	47
Other views for scaling and splitting the graph	53
About the numeric view	56
Setting up the table (Numeric view setup)	56
Exploring the table of numbers	57
Building your own table of numbers	59
“Build Your Own” menu keys	60
Example: plotting a circle	60
Function aplet	63
About the Function aplet	63
Getting started with the Function aplet	63
Function aplet interactive analysis	71
Plotting a piecewise-defined function	74
Parametric aplet	75
About the Parametric aplet	75
Getting started with the Parametric aplet	75
Polar aplet	79
Getting started with the Polar aplet	79
Sequence aplet	81
About the Sequence aplet	81
Getting started with the Sequence aplet	81
Solve aplet	85
About the Solve aplet	85
Getting started with the Solve aplet	86
Use an initial guess	89
Interpreting results	90
Plotting to find guesses	91
Using variables in equations	94
Linear Solver aplet	95
About the Linear Solver aplet	95
Getting started with the Linear Solver aplet	95
Triangle Solve aplet	99
About the Triangle Solver aplet	99
Getting started with the Triangle Solver aplet	99
Statistics aplet	103
About the Statistics aplet	103
Getting started with the Statistics aplet	103
Entering and editing statistical data	108
Defining a regression model	114
Computed statistics	116
Plotting	117
Plot types	118
Fitting a curve to 2VAR data	119
Setting up the plot (Plot setup view)	120
Trouble-shooting a plot	121
Exploring the graph	121
Calculating predicted values	122
Inference aplet	125
About the Inference aplet	125
Getting started with the Inference aplet	125
Importing sample statistics from the Statistics aplet	128
Hypothesis tests	132
One-Sample Z-Test	132
Two-Sample Z-Test	133
One-Proportion Z-Test	134
Two-Proportion Z-Test	135
One-Sample T-Test	136
Two-Sample T-Test	138
Confidence intervals	139
One-Sample Z-Interval	139
Two-Sample Z-Interval	140
One-Proportion Z-Interval	141
Two-Proportion Z-Interval	141
One-Sample T-Interval	142
Two-Sample T-Interval	143
Using the Finance Solver	145
Background	145
Performing TVM calculations	148
Calculating Amortizations	151
Using mathematical functions	153
Math functions	153
The MATH menu	153
Math functions by category	154
Keyboard functions	155
Calculus functions	158
Complex number functions	159
Constants	160
Conversions	160
Hyperbolic trigonometry	161
List functions	162
Loop functions	162
Matrix functions	163
Polynomial functions	163
Probability functions	164
Real-number functions	165
Two-variable statistics	169
Symbolic functions	169
Test functions	170
Trigonometry functions	171
Symbolic calculations	172
Finding derivatives	173
Program constants and physical constants	176
Program constants	176
Physical constants	177
Variables and memory management	179
Introduction	179
Storing and recalling variables	180
The VARS menu	182
Memory Manager	187
Matrices	189
Introduction	189
Creating and storing matrices	190
Working with matrices	192
Matrix arithmetic	194
Solving systems of linear equations	196
Matrix functions and commands	198
Argument conventions	198
Matrix functions	198
Examples	201
Lists	205
Displaying and editing lists	208
Deleting lists	210
Transmitting lists	210
List functions	210
Finding statistical values for list elements	213
Notes and sketches	215
Introduction	215
Aplet note view	215
Aplet sketch view	217
The notepad	220
Programming	223
Introduction	223
Program catalog	224
Creating and editing programs	226
Using programs	229
Customizing an aplet	231
Aplet naming convention	232
Example	232
Programming commands	235
Aplet commands	236
Branch commands	239
Drawing commands	241
Graphic commands	243
Loop commands	245
Matrix commands	246
Print commands	248
Prompt commands	248
Stat-One and Stat-Two commands	252
Stat-Two commands	252
Storing and retrieving variables in programs	253
Plot-view variables	254
Symbolic-view variables	261
Numeric-view variables	263
Note variables	266
Sketch variables	266
Extending aplets	267
Creating new aplets based on existing aplets	267
Using a customized aplet	269
Resetting an aplet	269
Annotating an aplet with notes	270
Annotating an aplet with sketches	270
Downloading e-lessons from the web	270
Sending and receiving aplets	270
Sorting items in the aplet library menu list	272
Reference information	273
Glossary	273
Resetting the hp 39gs	275
To erase all memory and reset defaults	275
If the calculator does not turn on	276
Operating details	276
Batteries	276
Variables	278
Home variables	278
Function aplet variables	279
Parametric aplet variables	280
Polar aplet variables	281
Sequence aplet variables	282
Solve aplet variables	283
Statistics aplet variables	284
MATH menu categories	285
Math functions	285
Program constants	287
Physical Constants	288
Program commands	289
Status messages	290
Limited Warranty	293
Service	295
Regulatory information	297
Index	301

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15-12

Matrices

LU Decomposition. Factors a square

matrix

into three

matrices:

{[[

lowertriangular

]],[[

uppertriangular

]],[[

permutation

]]}

The

uppertriangular

has ones on its diagonal.

(

matrix

)

MAKEMAT

Make Matrix. Creates a matrix of dimension

rows

columns

, using

expression

to calculate each element. If

expression

contains the variables I and J, then the

calculation for each element substitutes the current row

number for I and the current column number for J.

MAKEMAT

(

expression

rows

columns

)

Example

MAKEMAT(0,3,3)

returns a 3×3 zero matrix,

[[0,0,0],[0,0,0],[0,0,0]]

QR Factorization. Factors an

n matrix

into three

matrices:

{[[

orthogonal

]],[[

uppertrapezoidal

]],[[

n permutation

]]}.

(

matrix

)

RANK

Rank of a rectangular

matrix

RANK

(

matrix

)

ROWNORM

Row Norm. Finds the maximum value (over all rows) for

the sums of the absolute values of all elements in a row.

ROWNORM

(

matrix

)

RREF

Reduced-Row Echelon Form. Changes a rectangular

matrix

to its reduced row-echelon form.

RREF

(

matrix

)

SCHUR

Schur Decomposition. Factors a square

matrix

into two

matrices. If

matrix

is real, then the result is

{[[

orthogonal

]],[[

upper-quasi triangular

]]}.

matrix

is complex, then the result is

{[[

unitary

]],[[

upper-triangular

]]}.

SCHUR

(

matrix

)

SIZE

Dimensions of

matrix

. Returned as a list: {rows,columns}.

SIZE

(

matrix

)