Rank, Rownorm, Rref, Schur, Size, Specnorm | HP 39g+ Graphing

	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	QR Factorization. Factors an m×n matrix into three
	matrices: {[[m×m orthogonal]],[[m×n
	uppertrapezoidal]],[[n×n permutation]]}.
	QR(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]]}.
	If matrix is complex, then the result is
	{[[unitary]],[[upper-triangular]]}.
	SCHUR(matrix)
SIZE	Dimensions of matrix. Returned as a list: {rows,columns}.
	SIZE(matrix)
SPECNORM	Spectral Norm of matrix.
	SPECNORM(matrix)
SPECRAD	Spectral Radius of a square matrix.
	SPECRAD(matrix)

13-12

Matrices

Image 190

HP 39g+ Graphing manual Rank, Rownorm, Rref, Schur, Size, Specnorm, Specrad

Contents

User’s guide Edition Part Number F2224-90001 Printing History Edition December Contents About the Solve aplet Using variables in equationsPlotting a piecewise-defined function Getting started with the Polar aplet 10-7 Confidence intervals One-Sample Z-IntervalOne-Proportion Z-Interval 11-1 Variables and memory management Creating and editing programs 16-4 16-116-2 16-7 Operating details Glossary Resetting the hp 39g+Service Regulatory information Variables Home variables Hewlett Packard’s Calculators web site can be found at PrefaceManual conventions Function, Polar, Parametric Preface Getting started On/off, cancel operationsTo cancel To turn on Parts of the display To adjustDisplay Contrast Menu keys KeyboardInfrared or cable Aplet control keys Displays the Aplet Library menu. See Aplet library on Same Entry/Edit keysButton performs Shifted keystrokes Helpwith Math keys Program CommandsMenus Inactive keys Reset input form values Input forms Current aplet and Home give Mode settingsYou use the Modes input form to set the modes for Home Same result Lists and matrices, and to separate Setting Options NumberFunction arguments. Comma mode Uses periods dot as separators Aplets E-lessons Setting a modePress to return to Home Sequence Sequence functions U in terms of n, or Example x = cost and y = sintPolar Another sequence, such as Un 1 Quad Explorer aplet Amplitude and frequency Keys Transforms Graph, with theseSeen by experimenting Aplet library Symbolic viewAplet views Select Plot-Table Plot view Numeric view Plot-Table view Plot-Detail viewSelect Plot-Detail Overlay Plot view Sketch view Aplet view configurationPlot Setup Views menu contains the Overlay Plot view Mathematical calculations Numeric Setup Symbolic SetupWhere to start Entering expressions Using Long results Negative numbers Scientific notation powers23 3 EEX Parentheses Explicit and implicit multiplicationEntering Calculates Sin 45 + π Input Output Last input Edit line Last output Getting started Storing a value in a variable Accessing the display history Clearing the display history Using fractionsSetting Fraction mode Setting fraction precision Select Fraction calculationsFraction Converting decimals to fractions Complex numbers Catalogs and editors Aplets and their views About the Symbolic viewDefining an expression Symbolic view Aplet views Independent variable in the expressions is T U0. Define the nth term Aplets Evaluating expressionsSelect Function Home Setting up the plot Plot view setup About the Plot view ΘRNG Plot view settingsΘSTEP Reset plot settings Exploring the graph Trace a graph To move between relations To jump directly to a value To turn trace on/off Zoom within a graphZoom options Factors SquareSet Auto Scale Un-zoom Now un-zoom One diagonal of the zoom rectangle To box zoomBox Zoom option lets you draw a box around To turn on the menu-key Press to zoom in on the boxed area Other views for scaling and splitting the graph Views menu options Pixel=π/24 radian, 7.58, or Split the screenPress or About the numeric view Setting up the table Numeric view setup Numeric view settings NUM view menu keys Zoom within a table Exploring the table of numbersNumstart and Numstep Build a table Building your own table of numbersNumtype Build Your Own Build Your Own menu keys Clear data Plot the circle, x 2+ y 2 = 9. First rearrange it to read Reset the graph setup to the default settingsExample plotting a circle Function aplet, specify the functions Display the functions in numeric form Getting started with the Function aplet Function apletAbout the Function aplet Open the Function aplet Specify a grid for the graph Define the expressions Set up the plotPlot the functions Plot the functions Scale Change the scale Trace a graphSelect Auto Times Analyse graph with FCN functions Select Root Select Slope Select Signed area To find the extremum of the quadratic Select Extremum Explore the table Display the numeric viewDisplay the table of values Symbolic definition F1 is displayed at Bottom of the screen Symbolic definition A columnDisplay the symbolic definition for the F1 column To display Select Plot FCN Function aplet interactive analysisOr to choose a variable Extremum FCN functionsRoot Slope Intersection Symbolic view. DisplaysShading area Cursor. You need to have at Plotting a piecewise-defined function Getting started with the Parametric aplet Parametric apletAbout the Parametric aplet Define the expressions Set the angle measure to degrees Set up the plot Plot the expressionSet angle measure Select Degrees Plot a triangle graph over the existing circle graph Overlay plot Display the numbers120 Page Open the Polar aplet Polar apletGetting started with the Polar aplet Select Polar Explore the graph Display the numbers Display the Plot view menu key labels About the Sequence aplet Sequence aplet starts in the Symbolic viewSequence aplet Getting started with the Sequence aplet Plot Setup, set the Seqplot option to Cobweb Menu keys to assist in the entry of equations Select Cobweb Display the . Display the table of values for this examplePage Solve aplet About the Solve aplet Define the equation Enter known variables Getting started with the Solve apletOpen the Solve aplet Select Solve Solve the unknown variable Plot the equation Select Auto Scale Use an initial guess Interpreting results Plotting to find guesses Consider the equation of motion for an accelerating body To highlight T Plot the graph Press until the cursor is at the intersection Using variables in equations About the Statistics aplet Statistics apletGetting started with the Statistics aplet Select Statistics Enter dataTo move to the next column Select Linear Select a fit in the Symbolic setup viewChoose fit and data columns Explore statistics Value is To move to the FIT1 field Setup plot Plot the graph Draw the regression curveDisplay the equation for best linear fit Slope m is 425.875. The y-intercept b is Predict values To highlight Entering and editing statistical data Statistics aplet’s Numeric view keys are Statistics Copies the column variable or Variable expression to the edit line Data sets will need to be selected Clear is usedAgain before re-use Save data Plot a histogram of the data Edit a data set Delete data Insert data Sort data values To choose the fit Angle SettingDefining a regression model Fit models Computed statistics To define your own fit 7,8,15,16,17 Two-variableΣX2 To plot statistical data PlottingColumns for a linear fit only Plot types Histogram Box and Whisker Plot Scatter Plot Fitting a curve to 2VAR data Relative ErrorCorrelation coefficient Trouble-shooting a plot Setting up the plot Plot setup viewHistogram range Plotting mark 2VAR Connected points 2VAR Statistics aplet’s Plot view keys Erases the plot Calculating predicted values Find predicted values Statistics aplet Page Getting started with the Inference aplet Inference apletAbout the Inference aplet Open the Inference aplet Table below summarizes the options available Symbolic view Inference aplet’s Symb view keys Select Hypoth Test Setup-NUMSelect the inferential method Enter data Test 1 ∝ Are explained in the feature of this aplet Importing sample statistics from the Statistics aplet C1 column, enter the random numbers If the Decimal Mark setting in the Modes input formStatistics aplet opens in the Numeric view Produced by the calculator 529 295 952 259 925 592 Inference Set up the interval calculationOpen Inference aplet Select Conf Interval Specify a 90% Confidence interval in the C field Display Numeric view Display Plot viewTo move to the C field Menu name Hypothesis testsOne-Sample Z-Test Inputs Two-Sample Z-Test Results Test 1π One-Proportion Z-TestPopulation 2 standard Measures the strength of the evidence for a selected Two-Proportion Z-Test One-Sample T-Test Sample standard deviation With the α level that you Two-Sample T-Test Pooled? Confidence intervals One-Sample Z-Interval Two-Sample Z-Interval One-Proportion Z-Interval Two-Proportion Z-Interval One-Sample T-Interval Two-Sample T-Interval Pooled Critical T Critical value for T Using the Finance Solver Background 3 4 Compounding period -- which is Performing TVM calculations Example 1 Loan calculations Soft menu key. The resulting value is PV = $15,705.85 Example 2 Mortgage with balloon payment Example 3 Amortization for home mortgage Calculating AmortizationsTo calculate amortizations To continue amortizing the loan Example 4 Amortization for home mortgage Math menu Using mathematical functionsMath functions Name. Note You do not need to press first Syntax Math functions by categoryFunction categories Functions common to keyboard and menus Evalue Keyboard functionsValue1+ value2 , etc E5 returns Returns LOG100 returns ABS1,2 returns ∂ s1s1 2+3*s1 returns 2*s1+3 Calculus functionsNthroot 8 returns S1,2*X+3,X ARG Complex number functionsTaylor Conj Constants Hyperbolic trigonometry List functions Loop functions Polycoef Matrix functionsPolynomial functions POLYCOEF2,-3,4,-5 returns1,2,-25 Polyform PolyevalPolyroot Perm Probability functionsComb Random Real-number functions HMS→ FnrootFrac →HMS MOD MAXMIN Change Sign Two-variable statisticsRound Truncate LINEAR? Symbolic functionsIsolate Quad Test functions Quote Trigonometry functions SEC Symbolic calculationsUsing formal variables SECvalue Finding derivatives Symbolic calculations in the Function apletTo find derivatives in Home Select F2X and evaluate it To find derivatives in the Function aplet’s Symbolic viewShow the result You could also just define For example, to find the indefinite integral To find the indefinite integral using formal variablesThus, substituting X for S1, it can be seen that 11-24 Variables and memory management Introduction Storing and recalling variables You can use variables in calculations. The calculator To use variablesCalculations Substitutes the variable’s value in the calculation Press Vars menuOpen the Vars menu Move the highlight to the variables column Example Add the contents of two list variables, and to storeNames or values of variables into programs Result in another list variable 12-6 Variable on page 15-5 for more That you can configure usingReal part, and i represents Information on storing graphic object via Variable To access an apletX0, Y0 to X9, Y9 Symbolic view. See Aplet variables on page R-7 Memory Manager Line, press and pressPage Matrices MatricesVectors Matrix Variables Matrix Catalog keys Creating and storing matricesPOLYROOT1,0,-1,0XM1 To create a matrix in the Matrix Catalog To transmit a matrix Working with matricesOr column you are prompted to Make a choice Key Meaning Moves to the first row, last row, first If M2 is 3,4,5,6, then M21,2 returns To store one element Matrix arithmeticCreate the second matrix Matrices 13-7 To negate each Solving systems of linear equationsElement About functions Matrix functions and commandsSelect Real matrix Cond Argument conventionsColnorm Cross Eigenval DETDOT Eigenvv Rref RankRownorm Schur SVL ExamplesSVD Trace Reduced-Row Echelon Form Following set of equations x 2y + 3z = 14 2x + y z = Lists You can create, edit, delete, send, and receive named List catalog keys Create a list List edit keys To display one Displaying and editing listsTo display a list To edit a list Press , and press A listTo insert an element 1. Open the List catalog 148 L12 Transmitting lists List functionsDeleting lists To delete a list CONCAT1,2,3,4 returns 1,2,3,4 2,3 returns 5,10,15CONCATlist1,list2 ∆LISTlist1 POSlist, element ΠLISTlistΠLIST2,3,4 returns POS 3, 7, 12, 19,12 returns Sorts elements in ascending order. SORTlist Finding statistical values for list elementsΣLIST2,3,4 returns List, L1 Create L1 with values 88, 90, 89, 65, 70, Are now in column 1 C1 Your work is automatically saved. Press any view key Aplet note viewTo write a note in Note view Or to exit the Notes view Space key for text entry Contents of variablesCommands Alpha-lock for letter entry Sketch keys Aplet sketch viewTo draw a line To draw a box Draw keys Press to continue drawing, or press Mynote For a name Opens the selected note forBegins a new note, and asks Another hp 39g+ or PC Press instead Contents of a Program Structured Programming Programming Be simple-or it can be divided further into other Program catalogOpen Program Catalog Programs that perform smaller tasks Program catalog keys Create a new program Creating and editing programsPress Progrm to open the Program catalog Press to paste the command into the program editor On the left, use or to highlight a commandEdit a program 1. Press Progrm to Editing keys Using programs Run a program Debug a program Stop a program Transmit a program Customizing an aplet Aplet naming convention Example Configuring the Setviews menu option programs Save the aplet ’’My Entry2’’’’EXP.ME2’’3 Setviews ’’’’ ’’’’18’’My Entry1’’’’EXP.ME1’’1 ’’ ’’’’EXP.SV’’0 ’’’’’’EXP.ANG’’0 Programming commands’’START’’’’EXP.S’’7 Select Aplet commandsCheck Setviews Associating programs with your aplet Auto-run programs ViewNumber ProgramNameIncluding standard menu options Uncheck n Branch commandsIF...THEN...END 1XA END CASE...END Iferr Then Iferr trap-clause Then error-clause ENDIF... THEN... Else END Stop Drawing commandsRUN ARC Graphic commands Grobnot →DISPLAY→GROB Grobor Loop commands Do a + 1 X a Until a == Matrix commands Editmat DelcolDelrow Randmat Print commands Prompt commands Disptime ChooseDisp Disp 3A is 2+2 Input Input nametitle,labelhelpdefaultGetkey Editmat matrixname Prompt Stat-One and Stat-Two commandsMsgbox Wait Stat-One commands Stat-Two commands Area Storing and retrieving variables in programsPlot-view variables Axes FastRes CoordExtremum Grid InvCross HwidthIndep Isect Root Nmin / NmaxRecenter S1mark-S5mark StatPlot SimultSlope Umin/Umax Tstep Tmin / TmaxTracing Xcross Xmin / Xmax XtickYtick Ymin / Ymax Symbolic-view variables E1...E9, E0 R1...R9, R0U1...U9, U0 S1fit...S5fit Digits Numeric-view variablesC1...C9, C0 Format NumIndep NumColNumFont NumRow NumZoom NumStepNumType StatMode Graphicname X Sketch variablesPageNum PageNum Extending aplets Creating new aplets based on existing aplets Solve Open the Solve aplet and save it under the new nameDegrees Using a customized aplet Resetting an apletChoose the sine formula in E1 Sending and receiving aplets Downloading e-lessons from the webHewlett-Packard’s Calculators web site can be found at Sorting items in the aplet library menu list To transmit an aplet To sort the aplet list To delete an aplet Expression line# Reference informationGlossary Cross matrix1,matrix2 Vector One-dimensional array of values Editor and catalog Matrix Two-dimensional array of valuesRecord using the Program editor Set to Comma and enclosed To reset using the keyboard Resetting the hp 39g+To erase all memory and reset defaults Split screens If the calculator does not turn on Operating detailsBatteries To install the main batteries To install the backup battery Variables Home variables Area Root Extremum Slope Isect Function aplet variablesAngle Parametric aplet variables Parametric aplet variables are Category Available name Plot Polar aplet variables Polar aplet variables are Category Available names Plot Sequence aplet variables Sequence aplet variables are Category Available name Plot Solve aplet variables are Category Available name Plot Solve aplet variablesDigits NumCol Format NumRow Statistics aplet variables Math functions are Category Available name Calculus Math menu categoriesMath functions Hyperb Category Available name Matrix Polynom Program constants Branch Program commandsProgram commands are Category Command Aplet Print Status messages Current screen Function value, root, extremumOr intersection is not visible Such as 0/0 Limiting Warranty Hp 39g+ Graphing Calculator Warranty period 12 months Limiting Warranty Service Canada 905 206-4663 or Rotc = Rest of the country Regulatory information USA Limiting Warranty Index Maximum real number 11-8 minimum real number Freeze 16-20 Line 16-20 Pixoff 16-20 Pixon 16-20 Tline Grobor Grobxor Inverse hyperbolic cosine 11-8 inverse hyperbolic functions Break Angle measure 1-10 decimal mark 1-11 number format Order of precedence 1-21 overlaying plots 2-16,4-3 11-8 Sending and receiving 16-8 structured Menu lists 1-8 speed searches Navigate around 3-8 numeric values 3-7 numeric view setup Index