Cij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n | HP 49g instruction

Matrix multiplication

Matrix multiplication is defined by Cm×n = Am×p⋅Bp×n. Notice that matrix multiplication is only possible if the number of columns in the first operand is equal to the number of rows of the second operand. The general term in the product, cij, is defined as

p

cij = ∑aik ⋅ bkj , for i = 1,2,K, m; j = 1,2,K, n.

k=1

Matrix multiplication is not commutative, i.e., in general, A⋅B ≠ B⋅A. Furthermore, one of the multiplications may not even exist. The following screen shots show the results of multiplications of the matrices that we stored earlier:

Term-by-term multiplication

Term-by-term multiplication of two matrices of the same dimensions is possible through the use of function HADAMARD. The result is, of course, another matrix of the same dimensions. This function is available through Function catalog (‚N), or through the MATRICES/OPERATIONS sub-menu („Ø). Applications of function HADAMARD are presented next:

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HP 49g manual Cij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n

Contents

User’s manual Hp 49g+ graphing calculator Printing History Preface Table of Contents Calculations with real numbers Algebraic and arithmetic operations Calculations with complex numbers Operations with lists Solution to equations Matrices and linear algebra Vectors Calculus Applications GraphicsMulti-variate Calculus Applications Vector Analysis Applications Probability Distributions Differential EquationsStatistical Applications Limited Warranty W-1 Using SD cardsNumbers in Different Bases Basic Operations Chapter Getting startedBatteries Contents of the calculator’s display Tool menu Menus Introducing the calculator’s keyboard Setting time and datePage Selecting calculator modes Operating Mode √ 3.*5.-1/3.*3./23.3+EXP2.5 Lets try now the expression proposed earlier Number Format and decimal dot or comma Page Page Page Angle Measure Coordinate System Selecting CAS settings Selecting Display modes Explanation of CAS settings Selecting the display font Selecting properties of the line editor Selecting properties of the Stack Selecting properties of the equation writer EQW References Calculator objects Chapter Introducing the calculatorEditing expressions in the stack Creating arithmetic expressionsPage Page 2L 1 + + 2 L + y Creating algebraic expressions Using the Equation Writer EQW to create expressions Page + 2 ⋅ 5 + + e  x + 2µ ⋅ ∆y  Home directory Organizing data in the calculatorSubdirectories Typing variable names Variables Creating variables Page Page Checking variables contents Page Deleting variables Using function Purge in the stack in Algebraic mode Undo and CMD functions Using function Purge in the stack in RPN modeChoose boxes vs. Soft Menu Show Prog menu list and select Memory Page References Examples of real number calculations Chapter Calculations with real numbersPage Page Using powers of 10 in entering data Page Hyperbolic functions and their inverses Real number functions in the MTH menuPage Units menu Operations with unitsPage Available units Attaching units to numbers Operations with units Page Unit conversions Physical constants in the calculator Engl Defining and using functions ‘LNx+1 + EXPx ‘ Reference Chapter Calculations with complex numbers Setting the calculator to Complex modeDefinitions Polar representation of a complex number Entering complex numbers Simple operations with complex numbers Cmplx menu through the MTH menu Cmplx menus Cmplx menu in keyboard Function Droite equation of a straight line Functions applied to complex numbers Reference Entering algebraic objects Chapter Algebraic and arithmetic operations Simple operations with algebraic objects `‚¹ Collect Functions in the ALG menuPage Expansion and factoring using trigonometric functions Expansion and factoring using log-exp functionsOperations with transcendental functions Functions in the Arithmetic menu Horner function Polynomials Pcoef function VariableProot function Quot and Remainder functions Peval function FractionsSIMP2 function Partfrac function Propfrac functionFcoef function Froots function Step-by-step operations with polynomials and fractions− 5X 2 + 3X − Reference Symbolic solution of algebraic equations Chapter Solution to equationsFunction Isol Function Solve Page Function Zeros Function Solvevx Numerical solver menu @SOLVE@ Polynomial Equations Solve for coefficients ˜@SYMB@ Solving equations with one unknown through NUM.SLV Financial calculations Solution to simultaneous equations with Mslv Page Reference Creating and storing lists Chapter Operations with listsOperations with lists of numbers Changing sign Addition, subtraction, multiplication, division Functions applied to lists Lists of algebraic objects Lists of complex numbersMTH/LIST menu ∆LIST MAP function SEQ function Entering vectors Chapter VectorsTyping vectors in the stack Storing vectors into variables in the stack Using the Matrix Writer Mtrw to enter vectorsPage Page Addition, subtraction Simple operations with vectors Absolute value function Multiplication by a scalar, and division by a scalar Magnitude MTH/VECTOR menuDot product Cross product Chapter Matrices and linear algebra Using the Matrix WriterEntering matrices in the stack Typing in the matrix directly into the stack Addition and subtraction Operations with matrices Multiplication Cij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n Page Characterizing a matrix The matrix Norm menu Solution of linear systemsFunction DET Function Trace =  a Using the numerical solver for linear systems M x2 Solution by division of matrices Solution with the inverse matrix Graphs options in the calculator Chapter Graphics = 1 exp− x Plotting an expression of the form y = fx Generating a table of values for a function Page Fast 3D plots Left-1 Right1 Near-1 Far Low High Step Indep Depnd Page Reference Calc Calculus menu Chapter Calculus ApplicationsLimits and derivatives Function lim Functions Deriv and Dervx Xdx = F x + C Anti-derivatives and integralsFunctions INT, INTVX, RISCH, Sigma and Sigmavx Definite integrals Infinite series Functions TAYLR, TAYLR0, and Series Reference Partial derivatives Chapter Multi-variate Calculus Applications Φ x, ydydx Multiple integrals Del operator Chapter Vector Analysis ApplicationsGradient ∇ = i ⋅ ∂ + j ⋅ ∂ + k ⋅ ∂ ∂x ∂y ∂z Curl Divergence Chapter Differential Equations Solution to linear and non-linear equationsCALC/DIFF menu Function Ldec Yx = 5 ⋅ exp−x3 / 3 ⋅ expx3 / 3 ⋅ dx + C0 Function Desolve Desolve Variable Odetype Laplace transform and inverses in the calculator Laplace Transforms = ∑ c n Fourier seriesFunction Fourier Fourier series for a quadratic functionPage Reference MTH/PROBABILITY.. sub-menu part Chapter Probability DistributionsFactorials, combinations, and permutations − 2... − + 1 = − r Random numbers Normal distribution MTH/PROB menu partStudent-t distribution F distribution Chi-square distribution Entering data Chapter Statistical ApplicationsCalculating single-variable statistics Page Obtaining frequency distributions Fitting data to a function y = fx 195238095238 + 2.00857242857*X Correlation Covariance Obtaining additional summary statistics Confidence intervals Page Hypothesis testing Page Reference Base menu Chapter Numbers in Different BasesWriting non-decimal numbers HEX DEC OCT BIN Chapter Using SD cardsStoring objects in the SD card Purging an object from the SD card Recalling an object from the SD card Limited Warranty Service HP Invent USA Regulatory information