DoubleHermitianMatrix Class

Class DoubleHermitianMatrix represents a matrix of double-precision floating point complex values.

Inheritance Hierarchy

SystemObject
CenterSpace.NMath.CoreDoubleHermitianMatrix

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.3

Syntax

C++

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[SerializableAttribute]
public class DoubleHermitianMatrix : ICloneable

<SerializableAttribute>
Public Class DoubleHermitianMatrix
	Implements ICloneable

[SerializableAttribute]
public ref class DoubleHermitianMatrix : ICloneable

[<SerializableAttribute>]
type DoubleHermitianMatrix =  
    class
        interface ICloneable
    end

The DoubleHermitianMatrix type exposes the following members.

Constructors

	Name	Description
	DoubleHermitianMatrix(Int32)	Constructs a DoubleHermitianMatrix instance with the specified size.
	DoubleHermitianMatrix(DoubleComplexMatrix)	Constructs a square DoubleHermitianMatrix instance by extracting the upper triangular part of a square general matrix.
	DoubleHermitianMatrix(DoubleComplexVector)	Constructs a DoubleHermitianMatrix instance using the data in the given vector.
	DoubleHermitianMatrix(DoubleComplexVector, Int32)	Constructs a DoubleHermitianMatrix instance with the specified size, and using the data in the given vector.

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Properties

	Name	Description
	Cols	Gets the number of columns in the matrix.
	DataVector	Gets the data vector referenced by this matrix.
	Item	Gets and sets the value at the specified position. Symmetry is maintained.
	Order	Gets the order of the matrix.
	Rows	Gets the number of rows in the matrix.

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Methods

	Name	Description
	Add	Adds two Hermitian matrices.
	Clone	Creates a deep copy of this matrix.
	DeepenThisCopy	Guarantees that there is only one reference to the underlying data and that this data is in contiguous storage.
	Divide(DoubleComplex, DoubleHermitianMatrix)	Divide a scalar by an Hermitian matrix.
	Divide(DoubleHermitianMatrix, DoubleComplex)	Divide an Hermitian matrix by a scalar.
	Divide(DoubleHermitianMatrix, DoubleHermitianMatrix)	Divide an Hermitian matrix by another.
	Equals	Tests for equality of this matrix and another matrix. Two matrices are equal if they have the same dimensions and all values are equal. (Overrides ObjectEquals(Object).)
	GetHashCode	Returns an integer hash code for this matrix. (Overrides ObjectGetHashCode.)
	LeadingSubmatrix	Returns the k by k upper left corner of the matrix. The matrix and the submatrix share the same data.
	MakeDiagonalReal	Sets the imaginary parts on the main diagonal to zero thereby meeting the strict definition of an Hermitian matrix.
	Multiply(DoubleComplex, DoubleHermitianMatrix)	Multiply a scalar and an Hermitian matrix.
	Multiply(DoubleHermitianMatrix, DoubleComplex)	Multiply an Hermitian matrix and a scalar.
	Multiply(DoubleHermitianMatrix, DoubleHermitianMatrix)	Multiply two lower Hermitian matrices.
	Negate	Negation operator.
	OnDeserialized	Checks that the matrix is square following deserialization
	Resize	Changes the order of this matrix to that specified, adding zeros or truncating as necessary.
	ShallowCopy	Creates a shallow copy of this matrix.
	Subtract	Subtracts one Hermitian matrix from another.
	ToGeneralMatrix	Converts this Hermitian matrix to a general matrix.
	ToString	Returns a formatted string representation of this matrix. ToTabDelimited ToTabDelimited(String) (Overrides ObjectToString.)
	ToString(String)	Returns a formatted string representation of this matrix. Numbers are displayed using the specified format. ToTabDelimited ToTabDelimited(String)
	ToTabDelimited	Returns a formatted string representation of this matrix using tabs and newlines.
	ToTabDelimited(String)	Returns a formatted string representation of this matrix using tabs and newlines. Numbers are formatted using the specified format string.
	Transpose	Transposes the Hermitian matrix.

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Operators

	Name	Description
	Addition	Adds two Hermitian matrices.
	Division(DoubleComplex, DoubleHermitianMatrix)	Divide a scalar by an Hermitian matrix.
	Division(DoubleHermitianMatrix, DoubleComplex)	Divide an Hermitian matrix by a scalar.
	Division(DoubleHermitianMatrix, DoubleHermitianMatrix)	Divide an Hermitian matrix by another.
	Equality	Tests for equality of two Hermitian matrices. Two matrices are equal if they have the same order and all values are equal.
	(DoubleSymmetricMatrix to DoubleHermitianMatrix)	Implicitly converts a DoubleSymmetricMatrix instance into a DoubleHermitianMatrix instance.
	(FloatHermitianMatrix to DoubleHermitianMatrix)	Implicitly converts a FloatHermitianMatrix instance into a DoubleHermitianMatrix instance.
	Inequality	Tests for inequality of two Hermitian matrices. Two matrices are equal if they have the same order and all values are equal.
	Multiply(DoubleComplex, DoubleHermitianMatrix)	Multiply a scalar and an Hermitian matrix.
	Multiply(DoubleHermitianMatrix, DoubleComplex)	Multiply an Hermitian matrix and a scalar.
	Multiply(DoubleHermitianMatrix, DoubleHermitianMatrix)	Multiply two lower Hermitian matrices. Multiply two lower Hermitian matrices.
	Subtraction	Subtracts one Hermitian matrix from another.
	UnaryNegation	Negation operator.
	UnaryPlus	Unary + operator. Just returns the input matrix.

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Remarks

An Hermitian matrix is equal to its conjugate transpose. In other words, A[i,j] = conj(A[j,i]) for all elements i,j in matrix A.
The matrix is stored in a vector column by column. For efficiency, only the upper triangle is stored. For example, the following 5 by 5 Hermitian matrix:

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    | a00 a01 a02 a03 a04 |
    | a10 a11 a12 a13 a14 |
A = | a20 a21 a22 a23 a24 |
    | a30 a31 a32 a33 a34 |
    | a40 a41 a42 a43 a44 |

is stored in a data vector v as:

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v = [a00 a01 a11 a02 a12 a22 a03 a13 a23 a33 a04 a14 a24 a34 a44 ]

In general, A[i,j] = v[j(j+1)/2+i], i<=j conj(v[i(i+1)/2+j]), j<i

Reference

CenterSpace.NMath.Core Namespace