Record TC2MatrixQuantityHelper

Description
Methods

Unit

ADim

Declaration

type TC2MatrixQuantityHelper = record helper for TC2MatrixQuantity

Description

Record helper for TC2MatrixQuantity providing additional operations specific to 2×2 complex quantity matrices. Only available when ADIMOFF is not defined.

Overview

Methods

Public function Conjugate: TC2MatrixQuantity;
Public function Determinant: TComplexQuantity;
Public function Diagonalize(const AEigenvalues: TC2ArrayOfQuantity): TC2MatrixQuantity;
Public function Eigenvalues: TC2ArrayOfQuantity;
Public function Eigenvectors(const AEigenValues: TC2ArrayOfQuantity): TC2ArrayOfVector;
Public function Reciprocal(const ADeterminant: TComplexQuantity): TC2MatrixQuantity;
Public function TransposeConjugate: TC2MatrixQuantity;

Description

Methods

Public function Conjugate: TC2MatrixQuantity;

Returns the element-wise complex conjugate of the matrix. Each element a[i,j] = (x + i·y) [dim] becomes (x - i·y) [dim]. The physical dimension of each element is preserved.

Public function Determinant: TComplexQuantity;

Returns the determinant of the 2×2 complex quantity matrix. Defined as det(A) = a₁₁·a₂₂ - a₁₂·a₂₁. The resulting dimension is the square of the element dimension.

Public function Diagonalize(const AEigenvalues: TC2ArrayOfQuantity): TC2MatrixQuantity;

Returns the diagonal matrix built from the given eigenvalues. The result is a 2×2 diagonal TC2MatrixQuantity with the eigenvalues on the main diagonal and zeros elsewhere.

Parameters
AEigenvalues
The eigenvalues, typically computed via Eigenvalues.
Public function Eigenvalues: TC2ArrayOfQuantity;

Returns the eigenvalues of the 2×2 complex quantity matrix as a fixed-size array of TComplexQuantity. The eigenvalues carry the same dimension as the matrix elements.

Public function Eigenvectors(const AEigenValues: TC2ArrayOfQuantity): TC2ArrayOfVector;

Returns the eigenvectors of the 2×2 complex quantity matrix corresponding to the given eigenvalues, as a fixed-size array of dimensionless TC2Vector.

Parameters
AEigenValues
The eigenvalues, computed via Eigenvalues.
Public function Reciprocal(const ADeterminant: TComplexQuantity): TC2MatrixQuantity;

Returns the inverse of the matrix given its precomputed determinant. The resulting dimension is the inverse of the element dimension.

Parameters
ADeterminant
The determinant of the matrix, computed via Determinant.
Public function TransposeConjugate: TC2MatrixQuantity;

Returns the conjugate transpose (Hermitian adjoint) of the matrix: A† = (Aᵀ)* . Each element [i,j] of the result is the complex conjugate of [j,i] of the original. The physical dimension of each element is preserved.

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