NZMATH  1.2.0
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nzmath.matrix.FieldSquareMatrix Class Reference
Inheritance diagram for nzmath.matrix.FieldSquareMatrix:
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Collaboration diagram for nzmath.matrix.FieldSquareMatrix:
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Public Member Functions

def __init__ (self, row, column=0, compo=0, coeff_ring=0)
 
def triangulate (self)
 
def determinant (self)
 
def inverse (self, V=1)
 
def hessenbergForm (self)
 
def LUDecomposition (self)
 
- Public Member Functions inherited from nzmath.matrix.RingSquareMatrix
def __pow__ (self, other)
 
def toFieldMatrix (self)
 
def getRing (self)
 
def isOrthogonalMatrix (self)
 
def isAlternatingMatrix (self)
 
def isSingular (self)
 
def trace (self)
 
def cofactor (self, i, j)
 
def commutator (self, other)
 
def characteristicMatrix (self)
 
def characteristicPolynomial (self)
 
def adjugateMatrix (self)
 
def cofactorMatrix (self)
 
def smithNormalForm (self)
 
def extsmithNormalForm (self)
 
- Public Member Functions inherited from nzmath.matrix.SquareMatrix
def isUpperTriangularMatrix (self)
 
def isLowerTriangularMatrix (self)
 
def isDiagonalMatrix (self)
 
def isScalarMatrix (self)
 
def isSymmetricMatrix (self)
 
- Public Member Functions inherited from nzmath.matrix.Matrix
def __getitem__ (self, index)
 
def __setitem__ (self, key, value)
 
def __eq__ (self, other)
 
def __hash__ (self)
 
def __ne__ (self, other)
 
def __nonzero__ (self)
 
def __contains__ (self, item)
 
def __repr__ (self)
 
def __str__ (self)
 
def __call__ (self, arg)
 
def map (self, function)
 
def reduce (self, function, initializer=None)
 
def copy (self)
 
def set (self, compo)
 
def setRow (self, m, arg)
 
def setColumn (self, n, arg)
 
def getRow (self, i)
 
def getColumn (self, j)
 
def swapRow (self, m1, m2)
 
def swapColumn (self, n1, n2)
 
def insertRow (self, i, arg)
 
def insertColumn (self, j, arg)
 
def extendRow (self, arg)
 
def extendColumn (self, arg)
 
def deleteRow (self, i)
 
def deleteColumn (self, j)
 
def transpose (self)
 
def getBlock (self, i, j, row, column=None)
 
def subMatrix (self, I, J=None)
 
def toMatrix (self, flag=True)
 
- Public Member Functions inherited from nzmath.matrix.RingMatrix
def __add__ (self, other)
 
def __sub__ (self, other)
 
def __mul__ (self, other)
 
def __rmul__ (self, other)
 
def __mod__ (self, other)
 
def __pos__ (self)
 
def __neg__ (self)
 
def getCoefficientRing (self)
 
def hermiteNormalForm (self, non_zero=False)
 
def exthermiteNormalForm (self, non_zero=False)
 
def kernelAsModule (self)
 
- Public Member Functions inherited from nzmath.ring.RingElement
def __init__ (self, *args, **kwd)
 
def __eq__ (self, other)
 
def __hash__ (self)
 
def __ne__ (self, other)
 
- Public Member Functions inherited from nzmath.matrix.FieldMatrix
def __truediv__ (self, other)
 
def toSubspace (self, isbasis=None)
 
def kernel (self)
 
def image (self)
 
def rank (self)
 
def inverseImage (self, V)
 
def solve (self, B)
 
def columnEchelonForm (self)
 

Additional Inherited Members

- Public Attributes inherited from nzmath.matrix.RingSquareMatrix
 coeff_ring
 
 row
 
- Public Attributes inherited from nzmath.matrix.Matrix
 row
 
 column
 
 compo
 
 coeff_ring
 
- Public Attributes inherited from nzmath.matrix.RingMatrix
 row
 
 coeff_ring
 
- Public Attributes inherited from nzmath.matrix.FieldMatrix
 coeff_ring
 
 row
 
 isbasis
 
- Static Public Attributes inherited from nzmath.matrix.RingSquareMatrix
def isAntisymmetricMatrix = isAlternatingMatrix
 
def isSkewsymmetricMatrix = isAlternatingMatrix
 
def cofactors = cofactorMatrix
 
def SNF = smithNormalForm
 
def elementary_divisor = smithNormalForm
 
def extSNF = extsmithNormalForm
 
- Static Public Attributes inherited from nzmath.matrix.RingMatrix
def HNF = hermiteNormalForm
 
def extHNF = exthermiteNormalForm
 

Detailed Description

FieldSquareMatrix is a class for square matrices in field.

Definition at line 1431 of file matrix.py.

Constructor & Destructor Documentation

◆ __init__()

def nzmath.matrix.FieldSquareMatrix.__init__ (   self,
  row,
  column = 0,
  compo = 0,
  coeff_ring = 0 
)
FieldSquareMatrix(row [, column, components, coeff_ring])
FieldSquareMatrix must be row == column .

Reimplemented from nzmath.matrix.RingSquareMatrix.

Definition at line 1436 of file matrix.py.

References nzmath.matrix.Matrix._initialize().

Member Function Documentation

◆ determinant()

def nzmath.matrix.FieldSquareMatrix.determinant (   self)

◆ hessenbergForm()

def nzmath.matrix.FieldSquareMatrix.hessenbergForm (   self)

◆ inverse()

◆ LUDecomposition()

def nzmath.matrix.FieldSquareMatrix.LUDecomposition (   self)
LUDecomposition() -> (L, U)

L and U are matrices such that
    self == L * U
    L : lower triangular matrix
    U : upper triangular matrix

Definition at line 1564 of file matrix.py.

References nzmath.matrix.Matrix.coeff_ring, nzmath.factor.misc.FactoredInteger.copy(), nzmath.imaginary.Complex.copy(), nzmath.matrix.Matrix.copy(), nzmath.bigrange.range(), nzmath.matrix.Matrix.row, nzmath.lattice.LatticeElement.row, and nzmath.matrix.unitMatrix().

◆ triangulate()

def nzmath.matrix.FieldSquareMatrix.triangulate (   self)

The documentation for this class was generated from the following file: