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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: 19.4.401.0 (19.4.401.0)
Syntax
public struct Matrix3By3Symmetric : IEquatable<Matrix3By3Symmetric>, 
	IEquatable<Matrix3By3>

The Matrix3By3Symmetric type exposes the following members.

Constructors
  NameDescription
Public methodMatrix3By3Symmetric
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
  NameDescription
Public propertyStatic memberIdentity
Gets a Matrix3By3Symmetric representing an identity transformation.
Public propertyIsUndefined
Gets a value indicating whether any of the matrix values are NaN.
Public propertyItem
Accesses the matrix elements using zero-based indexing.
Public propertyM11
Gets the element in the first row, first column.
Public propertyM12
Gets the element in the first row, second column.
Public propertyM13
Gets the element in the first row, third column.
Public propertyM21
Gets the element in the second row, first column.
Public propertyM22
Gets the element in the second row, second column.
Public propertyM23
Gets the element in the second row, third column.
Public propertyM31
Gets the element in the third row, first column.
Public propertyM32
Gets the element in the third row, second column.
Public propertyM33
Gets the element in the third row, third column.
Public propertyStatic memberUndefined
Gets a Matrix3By3Symmetric with elements of NaN.
Public propertyStatic memberZero
Gets a Matrix3By3Symmetric representing the zero matrix.
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Methods
  NameDescription
Public methodAdd(Matrix3By3)
Adds a matrix to this matrix.
Public methodAdd(Matrix3By3Symmetric)
Adds a matrix to this matrix.
Public methodDeterminant
Calculates the determinant of the matrix.
Public methodStatic memberDiagonalMatrix(Cartesian)
Forms a diagonal matrix from the input vector.
Public methodStatic memberDiagonalMatrix(UnitCartesian)
Forms a diagonal matrix from the input unit vector.
Public methodStatic memberDiagonalMatrix(Double, Double, Double)
Forms a diagonal matrix from the input elements.
Public methodEigenDecomposition
Determines the eigenvectors and eigenvalues of the matrix. The eigenvalues appear in ascending order (smallest to largest) down the diagonal of the Values matrix.
Public methodEquals(Object)
Indicates whether another object is exactly equal to this instance.
(Overrides ValueTypeEquals(Object).)
Public methodEquals(Matrix3By3)
Indicates whether another instance of this type is exactly equal to this instance.
Public methodEquals(Matrix3By3Symmetric)
Indicates whether another instance of this type is exactly equal to this instance.
Public methodEqualsEpsilon
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.
Public methodFrobeniusNorm
Computes the Frobenius norm of the matrix.
Public methodFrobeniusNormSquared
Computes the square of the Frobenius norm of the matrix.
Public methodStatic memberFromLowerTriangular(Matrix3By3)
Forms a symmetric matrix from the lower triangular elements of the provided matrix.
Public methodStatic memberFromLowerTriangular(Double, Double, Double, Double, Double, Double)
Forms a symmetric matrix from the lower triangular elements.
Public methodStatic memberFromUpperTriangular(Matrix3By3)
Forms a symmetric matrix from the upper triangular elements of the provided matrix.
Public methodStatic memberFromUpperTriangular(Double, Double, Double, Double, Double, Double)
Forms a symmetric matrix from the upper triangular elements.
Public methodGetHashCode
Returns a hash code for this instance, which is suitable for use in hashing algorithms and data structures like a hash table.
(Overrides ValueTypeGetHashCode.)
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodInvert
Inverts the matrix.
Public methodMultiply(Double)
Multiplies this matrix by a scalar.
Public methodMultiply(Cartesian)
Forms a new Cartesian vector as the product of this 3-by-3 matrix and the provided Cartesian vector.
Public methodMultiply(Matrix3By3)
Multiplies this matrix by a matrix.
Public methodMultiply(Matrix3By3Symmetric)
Multiplies this matrix by a matrix.
Public methodSubtract(Matrix3By3)
Subtracts a matrix from this matrix.
Public methodSubtract(Matrix3By3Symmetric)
Subtracts a matrix from this matrix.
Public methodToString
Returns the fully qualified type name of this instance.
(Inherited from ValueType.)
Public methodTranspose
Transposes the matrix.
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Operators
  NameDescription
Public operatorStatic memberAddition(Matrix3By3Symmetric, Matrix3By3)
Adds a matrix to this matrix.
Public operatorStatic memberAddition(Matrix3By3Symmetric, Matrix3By3Symmetric)
Adds a matrix to this matrix.
Public operatorStatic memberEquality
Returns if the two instances are exactly equal.
Public operatorStatic memberInequality
Returns if the two instances are not exactly equal.
Public operatorStatic memberMultiply(Double, Matrix3By3Symmetric)
Multiplies a scalar by a matrix.
Public operatorStatic memberMultiply(Matrix3By3Symmetric, Cartesian)
Multiplies the 3-by-3 matrix by the Cartesian vector.
Public operatorStatic memberMultiply(Matrix3By3Symmetric, Matrix3By3)
Multiplies the left matrix by the right matrix.
Public operatorStatic memberMultiply(Matrix3By3Symmetric, Matrix3By3Symmetric)
Multiplies the left matrix by the right matrix.
Public operatorStatic memberMultiply(Matrix3By3Symmetric, Double)
Multiplies a matrix by a scalar.
Public operatorStatic memberSubtraction(Matrix3By3Symmetric, Matrix3By3)
Subtracts the second matrix from the first.
Public operatorStatic memberSubtraction(Matrix3By3Symmetric, Matrix3By3Symmetric)
Subtracts the second matrix from the first.
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See Also