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 "Complex Matrix" Complex Matrix Method
 RESULTS
 Original Matrix: m1 = (1 + 1 i, 1 + 2 i, 1 + 3 i 2 + 1 i, 2 + 2 i, 2 + 3 i 3 + 1 i, 3 + 2 i, 3 + 3 i) Original Matrix: m2 = (1 + 2 i, 7 - 3 i, 3 + 4 i 6 - 2 i, 0 + 9 i, 4 + 7 i 2 + 1 i, 3 - 1 i, 3 + 0 i) Original Vector: v = (1 + 1 i, 1 + 2 i, 1 + 3 i) m1 + m2 = (2 + 3 i, 8 - 1 i, 4 + 7 i 8 - 1 i, 2 + 11 i, 6 + 10 i 5 + 2 i, 6 + 1 i, 6 + 3 i) m1 - m2 = (0 - 1 i, -6 + 5 i, -2 - 1 i -4 + 3 i, 2 - 7 i, -2 - 4 i 1 + 0 i, 0 + 3 i, 0 + 3 i) m1 * m2 = (8 + 20 i, 22 - 11 i, -8 + 31 i 17 + 21 i, 32 - 6 i, 2 + 42 i 26 + 22 i, 42 - 1 i, 12 + 53 i) m2 * m1 = (21 + 19 i, 30 + 14 i, 15 + 41 i 4 + 47 i, 46 - 17 i, -24 + 67 i 17 + 7 i, 17 + 17 i, 17 + 23 i) m1 * v = (-11 + 12 i, -8 + 18 i, -5 + 24 i) v * m1 = (8 + 20 i, -2 + 21 i, -8 + 31 i) Determinant of m1 = 0 + 0 i Determinant of m2 = 109 + 201 i

 Vector V = (  +   i,   +   i,   +   i, )

IMPLEMENTATION
Complex Matrix Manipulation

As in the case of implementing a real matrix (Number Matrix Manipulation) a more complex matrix structure can be derived where matrices again can be added, multiplied and decomposed in many ways.

We show how to implement various complex matrix operations including matrix addition, subtraction, multiplication, transformation and determinant. A complex matrix can be created using either 2D complex array or by directly defining its matrix elements. Testing Complex Matrix Method

Supporting code and methods are not included.

As a sample we provide initial input data points using complex 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 new vector v values. The arrays themselves are fixed and no attempt was made to provide flexibility for input.

 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

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EIGENVALUE SOLUTIONS...
Eigen Inverse Iteration
Rayleigh-Quotient Method

INTERPOLATION APPLICATIONS...
Cubic Spline Method
Newton Divided Difference

 Applied Mathematical Algorithms Complex Functions A complex number z = x + iy, where... Complex Functions Non-Linear Systems Non-linear system methods... Non Linear Systems Differentiation Construction of differentiation... Differentiation Integration Consider the function where... Integration