Record TC3MatrixHelper

Description
Methods

Unit

ADim

Declaration

type TC3MatrixHelper = record helper for TC3Matrix

Description

Record helper for TC3Matrix providing additional operations specific to 3×3 complex matrices.

Overview

Methods

Public function Conjugate: TC3Matrix;
Public function Determinant: TComplex;
Public function Diagonalize(const AEigenValues: TC3ArrayOfComplex): TC3Matrix;
Public function Eigenvalues: TC3ArrayOfComplex;
Public function Eigenvectors(const AEigenValues: TC3ArrayOfComplex): TC3ArrayOfVector;
Public function Identity: TC3Matrix;
Public function NullMatrix: TC3Matrix;
Public function Reciprocal(const ADeterminant: TComplex): TC3Matrix;
Public function ToString: string;
Public function ToString(APrecision, ADigits: integer): string;
Public function Transpose: TC3Matrix;
Public function TransposeConjugate: TC3Matrix;

Description

Methods

Public function Conjugate: TC3Matrix;

Returns the element-wise complex conjugate of the matrix.

Public function Determinant: TComplex;

Returns the determinant of the 3×3 complex matrix using cofactor expansion.

Public function Diagonalize(const AEigenValues: TC3ArrayOfComplex): TC3Matrix;

Returns the diagonal matrix built from the given eigenvalues.

Parameters
AEigenValues
The eigenvalues, typically computed via Eigenvalues.
Public function Eigenvalues: TC3ArrayOfComplex;

Returns the eigenvalues of the 3×3 complex matrix as a fixed-size array.

Public function Eigenvectors(const AEigenValues: TC3ArrayOfComplex): TC3ArrayOfVector;

Returns the eigenvectors of the 3×3 complex matrix corresponding to the given eigenvalues.

Parameters
AEigenValues
The eigenvalues, computed via Eigenvalues.
Public function Identity: TC3Matrix;

Returns the 3×3 identity matrix over ℂ. Diagonal elements are TComplex(Re=1, Im=0); all off-diagonal elements are zero. Satisfies I·A = A·I = A for any conforming 3×3 complex matrix A.

Public function NullMatrix: TC3Matrix;

Returns the 3×3 zero matrix over ℂ. All elements are set to TComplex(Re=0, Im=0).

Public function Reciprocal(const ADeterminant: TComplex): TC3Matrix;

Returns the inverse of the matrix given its precomputed determinant.

Parameters
ADeterminant
The determinant of the matrix, computed via Determinant.
Public function ToString: string;

Converts the matrix to its default string representation.

Public function ToString(APrecision, ADigits: integer): string;

Converts the matrix to a formatted string with controlled precision.

Parameters
APrecision
Number of significant digits.
ADigits
Minimum number of digits in the output.
Public function Transpose: TC3Matrix;

Returns the transpose of the 3×3 complex matrix.

Public function TransposeConjugate: TC3Matrix;

Returns the conjugate transpose (Hermitian adjoint) of the matrix: A† = (Aᵀ)"*". Each element [i,j] of the result is the conjugate of [j,i] of the original.

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