Matrix3By3Symmetric Structure

A 3-by-3 symmetric matrix. This type is often used to represent position covariance.

Namespace: AGI.Foundation.Coordinates
Assembly: AGI.Foundation.Core (in AGI.Foundation.Core.dll) Version: 24.2.419.0 (24.2.419.0)

Syntax

C++

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public struct Matrix3By3Symmetric : IEquatable<Matrix3By3Symmetric>, 
	IEquatable<Matrix3By3>, IEquatableEpsilon<Matrix3By3Symmetric>

Public Structure Matrix3By3Symmetric
	Implements IEquatable(Of Matrix3By3Symmetric), IEquatable(Of Matrix3By3), 
	IEquatableEpsilon(Of Matrix3By3Symmetric)

public value class Matrix3By3Symmetric : IEquatable<Matrix3By3Symmetric>, 
	IEquatable<Matrix3By3>, IEquatableEpsilon<Matrix3By3Symmetric>

[<SealedAttribute>]
type Matrix3By3Symmetric =  
    struct
        interface IEquatable<Matrix3By3Symmetric>
        interface IEquatable<Matrix3By3>
        interface IEquatableEpsilon<Matrix3By3Symmetric>
    end

The Matrix3By3Symmetric type exposes the following members.

Constructors

	Name	Description
	Matrix3By3Symmetric	Initializes this instance as a symmetrical matrix constructed from the given symmetrical or nearly symmetrical Matrix3By3. Mxy and Myx of this matrix will be equal to the average Mxy and Myx of the given matrix.

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Properties

	Name	Description
	Identity	Gets a Matrix3By3Symmetric representing an identity transformation.
	IsUndefined	Gets a value indicating whether any of the matrix values are NaN.
	Item	Accesses the matrix elements using zero-based indexing.
	M11	Gets the element in the first row, first column.
	M12	Gets the element in the first row, second column.
	M13	Gets the element in the first row, third column.
	M21	Gets the element in the second row, first column.
	M22	Gets the element in the second row, second column.
	M23	Gets the element in the second row, third column.
	M31	Gets the element in the third row, first column.
	M32	Gets the element in the third row, second column.
	M33	Gets the element in the third row, third column.
	Undefined	Gets a Matrix3By3Symmetric with elements of NaN.
	Zero	Gets a Matrix3By3Symmetric representing the zero matrix.

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Methods

	Name	Description
	Add(Matrix3By3)	Adds a matrix to this matrix.
	Add(Matrix3By3Symmetric)	Adds a matrix to this matrix.
	Determinant	Calculates the determinant of the matrix.
	DiagonalMatrix(Cartesian)	Forms a diagonal matrix from the input vector.
	DiagonalMatrix(UnitCartesian)	Forms a diagonal matrix from the input unit vector.
	DiagonalMatrix(Double, Double, Double)	Forms a diagonal matrix from the input elements.
	EigenDecomposition	Determines the eigenvectors and eigenvalues of the matrix. The eigenvalues appear in ascending order (smallest to largest) down the diagonal of the Values matrix.
	Equals(Matrix3By3)	Indicates whether another instance of this type is exactly equal to this instance.
	Equals(Matrix3By3Symmetric)	Indicates whether another instance of this type is exactly equal to this instance.
	Equals(Object)	Indicates whether another object is exactly equal to this instance. (Overrides ValueTypeEquals(Object).)
	EqualsEpsilon	Returns true if all of the elements of this matrix are within epsilon of the same elements of the specified matrix. That is, in order for the matrices to be considered equal (and for this function to return true), the absolute value of the difference between each of their elements must be less than or equal to epsilon.
	FrobeniusNorm	Computes the Frobenius norm of the matrix.
	FrobeniusNormSquared	Computes the square of the Frobenius norm of the matrix.
	FromLowerTriangular(Matrix3By3)	Forms a symmetric matrix from the lower triangular elements of the provided matrix.
	FromLowerTriangular(Double, Double, Double, Double, Double, Double)	Forms a symmetric matrix from the lower triangular elements.
	FromUpperTriangular(Matrix3By3)	Forms a symmetric matrix from the upper triangular elements of the provided matrix.
	FromUpperTriangular(Double, Double, Double, Double, Double, Double)	Forms a symmetric matrix from the upper triangular elements.
	GetHashCode	Returns a hash code for this instance, which is suitable for use in hashing algorithms and data structures like a hash table. (Overrides ValueTypeGetHashCode.)
	GetType	Gets the Type of the current instance. (Inherited from Object.)
	Invert	Inverts the matrix.
	Multiply(Cartesian)	Forms a new Cartesian vector as the product of this 3-by-3 matrix and the provided Cartesian vector.
	Multiply(Double)	Multiplies this matrix by a scalar.
	Multiply(Matrix3By3)	Multiplies this matrix by a matrix.
	Multiply(Matrix3By3Symmetric)	Multiplies this matrix by a matrix.
	Subtract(Matrix3By3)	Subtracts a matrix from this matrix.
	Subtract(Matrix3By3Symmetric)	Subtracts a matrix from this matrix.
	ToString	Returns the fully qualified type name of this instance. (Inherited from ValueType.)
	Transpose	Transposes the matrix.

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Operators

	Name	Description
	Addition(Matrix3By3Symmetric, Matrix3By3)	Adds a matrix to this matrix.
	Addition(Matrix3By3Symmetric, Matrix3By3Symmetric)	Adds a matrix to this matrix.
	Equality	Returns if the two instances are exactly equal.
	Inequality	Returns if the two instances are not exactly equal.
	Multiply(Double, Matrix3By3Symmetric)	Multiplies a scalar by a matrix.
	Multiply(Matrix3By3Symmetric, Cartesian)	Multiplies the 3-by-3 matrix by the Cartesian vector.
	Multiply(Matrix3By3Symmetric, Matrix3By3)	Multiplies the left matrix by the right matrix.
	Multiply(Matrix3By3Symmetric, Matrix3By3Symmetric)	Multiplies the left matrix by the right matrix.
	Multiply(Matrix3By3Symmetric, Double)	Multiplies a matrix by a scalar.
	Subtraction(Matrix3By3Symmetric, Matrix3By3)	Subtracts the second matrix from the first.
	Subtraction(Matrix3By3Symmetric, Matrix3By3Symmetric)	Subtracts the second matrix from the first.

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Reference

AGI.Foundation.Coordinates Namespace