com.numericalmethod.suanshu.matrix.doubles

Interface MatrixRing

All Superinterfaces:

AbelianGroup<Matrix>, Monoid<Matrix>, Ring<Matrix>, java.io.Serializable

All Known Subinterfaces:

Matrix, SparseMatrix

All Known Implementing Classes:

BidiagonalMatrix, BorderedHessian, CholeskyWang2006, CongruentMatrix, CorrelationMatrix, CovarianceMatrix, CSRSparseMatrix, DenseMatrix, DiagonalMatrix, DOKSparseMatrix, FastKroneckerProduct, GivensMatrix, GoldfeldQuandtTrotter, Hessian, HilbertMatrix, ImmutableMatrix, Inverse, Jacobian, KroneckerProduct, LILSparseMatrix, LowerTriangularMatrix, MAT, MatthewsDavies, PermutationMatrix, PositiveDefiniteMatrixByPositiveDiagonal, PositiveSemiDefiniteMatrixNonNegativeDiagonal, Pow, PseudoInverse, SimilarMatrix, SubMatrixRef, SymmetricKronecker, SymmetricMatrix, TridiagonalMatrix, UpperTriangularMatrix

public interface MatrixRing
extends Ring<Matrix>

A matrix ring is the set of all n × n matrices over an arbitrary Ring R. This matrix set becomes a ring under matrix addition and multiplication. Moreover, it has a structure of a *-algebra over R, where the involution * on the matrix ring is the matrix transposition.

Method Summary

Modifier and Type	Method and Description
Matrix	add(Matrix that) this + that
Matrix	minus(Matrix that) this - that
Matrix	multiply(Matrix that) this * that
Matrix	ONE() Get an identity matrix that has the same dimension as this matrix.
Matrix	opposite() Get the opposite of this matrix.
Matrix	t() Get the transpose of this matrix.
Matrix	ZERO() Get a zero matrix that has the same dimension as this matrix.

Method Detail

t

Matrix t()

Get the transpose of this matrix. This is the involution on the matrix ring.

Returns:

the transpose of this matrix

add

Matrix add(Matrix that)

this + that

Specified by:

add in interface AbelianGroup<Matrix>

Parameters:

that - a matrix

Returns:

the sum of this and that

minus

Matrix minus(Matrix that)

this - that

Specified by:

minus in interface AbelianGroup<Matrix>

Parameters:

that - a matrix

Returns:

the difference between this and that

multiply

Matrix multiply(Matrix that)

this * that

Specified by:

multiply in interface Monoid<Matrix>

Parameters:

that - a matrix

Returns:

the product ofthis and that

opposite

Matrix opposite()

Get the opposite of this matrix.

Specified by:

opposite in interface AbelianGroup<Matrix>

Returns:

-this

See Also:

Wikipedia: Additive inverse

ZERO

Matrix ZERO()

Get a zero matrix that has the same dimension as this matrix.

Specified by:

ZERO in interface AbelianGroup<Matrix>

Returns:

the 0 matrix

ONE

Matrix ONE()

Get an identity matrix that has the same dimension as this matrix. For a non-square matrix, it zeros out the rows (columns) with index > nCols (nRows).

Specified by:

ONE in interface Monoid<Matrix>

Returns:

an identity matrix