Home Login  |   Contact  |   About Us       Tuesday, March 19, 2024   

j0185201- Back to Home
   Skip Navigation LinksHOME ›  AREAS OF EXPERTISE  #1 ›   Vectors / Matrices ›  ~ Matrix Manipulation



Skip Navigation Links.



"Number Matrix Manipulation"
Matrix Manipulator Method
Results =


Matrix m1 = { , , },{ , , }, , , }
Matrix m2 = { , , },{ , , }, , , }
Vector v = ( , , )


                                         

IMPLEMENTATION
Matrix Manipulation

A matrix can be used to describe linear equations, to keep track of the coefficients of the linear transformations and also to record data that depend on two parameters. Matrices can be added, multiplied and decomposed in many ways. Our sample involve square matrices. Although no details are given regarding the various operations, we do the following:

  • Vector from Matrix - in some instances we extract a vector from a row or column of a matrix.

  • Swap, Transpose and Trace - interchange two rows or two columns of a matrix as needed.

  • Transformations - often used when performing operations on graphic objects. In our case we implement matrix transformation for n-dimensional vectors and n by n matrices (squared matrices).

  • Matrix Multiplication - in our case the number of columns of the first matrix is the same as the number of rows of the second matrix.

  • Mathematical Operators - we implement various mathematical operations (see results above).

  • Determinant and Inverse - important qualities associated with square matrices.


Testing Matrix Operator Method

In order to test the Matrix Operator Method, a new TestMatrixOperators() static method has been added and executed. Supporting code and methods are not shown.

           static void TestMatrixOperators();
              {
                 ListBox1.Items.Clear();
                 MatrixR m1 = new MatrixR(new double[3, 3] { {t1, t2, t3}, {t4, t5, t6},
                       {t7, t8, t9}});
                 MatrixR m2 = new MatrixR(new double[3, 3] { {8, 1, 6}, {3, 5, 7},
                       {4, 9, 2}});
                 VectorR v = new VectorR(new double[] { t19, t20, t21 });
                 ListBox1.Items.Add(" matrix: m1 = " + m1);
                 ListBox1.Items.Add(" matrix: m2 = " + m2);
                 ListBox1.Items.Add(" vector: v = " + (v));
                 ListBox1.Items.Add("m1 + m2 = " + (m1 + m2));
                 ListBox1.Items.Add("m1 - m2 = " + (m1 - m2));
                 ListBox1.Items.Add("m1 * m2 = " + (m1 * m2));
                 ListBox1.Items.Add("m2 * m1 = " + (m2 * m1));
                 ListBox1.Items.Add("m1 * v = " + MatrixR.Transform(m1, v));
                 ListBox1.Items.Add("v * m1 = " + MatrixR.Transform(v, m2));
                 ListBox1.Items.Add("Inverse of m1 = " + MatrixR.Inverse(m1));
                 ListBox1.Items.Add("Inverse of m2 = " + MatrixR.Inverse(m2));
                 ListBox1.Items.Add("Determinant of m1 = " + MatrixR.Determinant(m1));
                 ListBox1.Items.Add("Determinant of m2 = " + MatrixR.Determinant(m2));
              }

As a sample we provide the input data points using double arrays for matrix m1, matrix m2 and vector v. Results of the various mathematical operators are shown on the screen above.

The user can manipulate matrix m1 and vector v values and try variations on the arrays themselves by specifying new matrix and vector values.



Other Implementations...


Object-Oriented Implementation
Graphics and Animation
Sample Applications
Ore Extraction Optimization
Vectors and Matrices
Complex Numbers and Functions
Ordinary Differential Equations - Euler Method
Ordinary Differential Equations 2nd-Order Runge-Kutta
Ordinary Differential Equations 4th-Order Runge-Kutta
Higher Order Differential Equations
Nonlinear Systems
Numerical Integration
Numerical Differentiation
Function Evaluation


   Quotes

Consulting Services - Back to Home


Home

Home Math, Analysis,
  expertise..."

EIGENVALUE
SOLUTIONS...


> Rayleigh-Quotient Method

> Cubic Spline Method

 

Applied Mathematical Algorithms

Home

ComplexFunctions

Home

NonLinear
Home

Differentiation
Home

Integration
About Us


KMP Software Engineering is an independent multidisciplinary engineering consulting company specializing in mathematical algorithms.

      (About Us) →
Areas of
Expertise


SpecialFunctions
VectorsMatrices
OptimizationMethods
ComplexNumbers
Interpolation
CurveFitting
NonLinearSystems
LinearEquations
DistributionFunctions
NumericalDifferentiation
NumericalIntegration
DifferentialEquations
Smalltalk
FiniteBoundary
Eigenvalue
Graphics
Understanding
Mining


MiningMastery
MineralNews
MineralCommodities
MineralForum
Crystallography
Services


NumericalModeling
WebServices
MainframeServices
OutsourceServices

LINKED IN
MINE REVIEW(by G.Pacheco)
Brand





Home

Login

Contact
Since 2006 All Rights Reserved  © KMP Software Engineering LINKS | PRIVACY POLICY | LEGAL NOTICE