Package org.drip.numerical.complex

Class C1CartesianFuhrRzeszotnik

java.lang.Object

org.drip.numerical.complex.C1Square

org.drip.numerical.complex.C1CartesianFuhrRzeszotnik

public class C1CartesianFuhrRzeszotnik
extends C1Square

C1CartesianFuhrRzeszotnik implements the type and Functionality associated with a C¹ Square Matrix parameterized by the Fuhr-Rzeszotnik parameters rho, epsilon, eta, and sigma Fields. The References are:

• Fuhr, H., and Z. Rzeszotnik (2018): A Note on Factoring Unitary Matrices Linear Algebra and its Applications 547 32-44
• Horn, R. A., and C. R. Johnson (2013): Matrix Analysis Cambridge University Press Cambridge UK
• Li, C. K., and E. Poon (2002): Additive Decomposition of Real Matrices Linear and Multilinear Algebra 50 (4) 321-326
• Marvian, I. (2022): Restrictions on realizable Unitary Operations imposed by Symmetry and Locality Nature Science 18 (3) 283-289
• Wikipedia (2024): Unitary Matrix https://en.wikipedia.org/wiki/Unitary_matrix

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = Implementation of Complex Number Suite

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
double	epsilon()	Retrieve Epsilon
double	eta()	Retrieve Eta
C1Square	jordanNormalCenter()	Retrieve the Jordan Normal Center Part of C1CartesianPhiPsiThetaDelta
R1SquareRotation2x2	jordanNormalLeft()	Retrieve the Jordan Normal Left Part of C1CartesianPhiPsiThetaDelta
R1SquareRotation2x2	jordanNormalRight()	Retrieve the Jordan Normal Right Part of C1CartesianPhiPsiThetaDelta
double	rho()	Retrieve Rho
double	sigma()	Retrieve Sigma
static C1CartesianFuhrRzeszotnik	Standard(double eta, double rho, double sigma, double epsilon)	Construct a Standard Instance of C1CartesianFuhrRzeszotnik

Methods inherited from class org.drip.numerical.complex.C1Square

c1Grid, determinant, isUnitary, isUnitDeterminant, product, product, product, Rotation2x2, Rotation2x2, size, slimContract, Standard, transpose

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

Standard

public static C1CartesianFuhrRzeszotnik Standard(double eta,
double rho,
double sigma,
double epsilon)

Construct a Standard Instance of C1CartesianFuhrRzeszotnik

Parameters:

eta - "Eta"

rho - "Rho"

sigma - "Sigma"

epsilon - "Epsilon"

Returns:

C1CartesianFuhrRzeszotnik Instance

rho

public double rho()

Retrieve Rho

Returns:

Rho

epsilon

public double epsilon()

Retrieve Epsilon

Returns:

Epsilon

eta

public double eta()

Retrieve Eta

Returns:

Eta

sigma

public double sigma()

Retrieve Sigma

Returns:

Sigma

jordanNormalLeft

public R1SquareRotation2x2 jordanNormalLeft()

Retrieve the Jordan Normal Left Part of C1CartesianPhiPsiThetaDelta

Returns:

Jordan Normal Left Part of C1CartesianPhiPsiThetaDelta

jordanNormalCenter

public C1Square jordanNormalCenter()

Retrieve the Jordan Normal Center Part of C1CartesianPhiPsiThetaDelta

Returns:

Jordan Normal Center Part of C1CartesianPhiPsiThetaDelta

jordanNormalRight

public R1SquareRotation2x2 jordanNormalRight()

Retrieve the Jordan Normal Right Part of C1CartesianPhiPsiThetaDelta

Returns:

Jordan Normal Right Part of C1CartesianPhiPsiThetaDelta