JuliaComplexF64SquareMatrix n

jarray64.spad line 990 [edit on github]

• n: NonNegativeInteger

This domain provides a fast Julia Float64 square matrix type with no bound checking on elt's. Minimum index is 1.

0: %

from AbelianMonoid

1: %

from MagmaWithUnit

#: % -> NonNegativeInteger

from Aggregate

*: (%, %) -> %

from Magma

*: (%, Integer) -> % if JuliaComplexF64 has LinearlyExplicitOver Integer

from RightModule Integer

*: (%, JuliaComplexF64) -> %

from RightModule JuliaComplexF64

*: (%, JuliaComplexF64Vector) -> JuliaComplexF64Vector

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

*: (Integer, %) -> %

from AbelianGroup

*: (JuliaComplexF64, %) -> %

from LeftModule JuliaComplexF64

*: (JuliaComplexF64Vector, %) -> JuliaComplexF64Vector

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

-: % -> %

from AbelianGroup

-: (%, %) -> %

from AbelianGroup

/: (%, JuliaComplexF64) -> %

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

=: (%, %) -> Boolean

from BasicType

^: (%, Integer) -> %

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

^: (%, NonNegativeInteger) -> %

from MagmaWithUnit

^: (%, PositiveInteger) -> %

from Magma

~=: (%, %) -> Boolean

from BasicType

annihilate?: (%, %) -> Boolean

from Rng

antiCommutator: (%, %) -> %

from NonAssociativeSemiRng

antisymmetric?: % -> Boolean

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

any?: (JuliaComplexF64 -> Boolean, %) -> Boolean

from HomogeneousAggregate JuliaComplexF64

associator: (%, %, %) -> %

from NonAssociativeRng

characteristic: () -> NonNegativeInteger

from NonAssociativeRing

coerce: % -> JuliaComplexF64Matrix

coerce(m) coerces m to JuliaComplexF64Matrix

coerce: % -> OutputForm

from CoercibleTo OutputForm

coerce: Fraction Integer -> %

from CoercibleFrom Fraction Integer

coerce: Integer -> %

from NonAssociativeRing

coerce: JuliaComplexF64 -> %

from Algebra JuliaComplexF64

column: (%, Integer) -> JuliaComplexF64Vector

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

columnSpace: % -> List JuliaComplexF64Vector

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

commutator: (%, %) -> %

from NonAssociativeRng

convert: % -> InputForm if JuliaComplexF64 has Finite

from ConvertibleTo InputForm

convert: % -> String

from ConvertibleTo String

copy: % -> %

from Aggregate

count: (JuliaComplexF64 -> Boolean, %) -> NonNegativeInteger

from HomogeneousAggregate JuliaComplexF64

count: (JuliaComplexF64, %) -> NonNegativeInteger

from HomogeneousAggregate JuliaComplexF64

D: % -> %

from DifferentialRing

D: (%, JuliaComplexF64 -> JuliaComplexF64) -> %

from DifferentialExtension JuliaComplexF64

D: (%, JuliaComplexF64 -> JuliaComplexF64, NonNegativeInteger) -> %

from DifferentialExtension JuliaComplexF64

D: (%, List Symbol) -> % if JuliaComplexF64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, List Symbol, List NonNegativeInteger) -> % if JuliaComplexF64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, NonNegativeInteger) -> %

from DifferentialRing

D: (%, Symbol) -> % if JuliaComplexF64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

D: (%, Symbol, NonNegativeInteger) -> % if JuliaComplexF64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

determinant: % -> JuliaComplexF64

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

diagonal?: % -> Boolean

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

diagonal: % -> JuliaComplexF64Vector

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

diagonalMatrix: List JuliaComplexF64 -> %

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

diagonalProduct: % -> JuliaComplexF64

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

differentiate: % -> %

from DifferentialRing

differentiate: (%, JuliaComplexF64 -> JuliaComplexF64) -> %

from DifferentialExtension JuliaComplexF64

differentiate: (%, JuliaComplexF64 -> JuliaComplexF64, NonNegativeInteger) -> %

from DifferentialExtension JuliaComplexF64

differentiate: (%, List Symbol) -> % if JuliaComplexF64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, List Symbol, List NonNegativeInteger) -> % if JuliaComplexF64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, NonNegativeInteger) -> %

from DifferentialRing

differentiate: (%, Symbol) -> % if JuliaComplexF64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

differentiate: (%, Symbol, NonNegativeInteger) -> % if JuliaComplexF64 has PartialDifferentialRing Symbol

from PartialDifferentialRing Symbol

elt: (%, Integer, Integer) -> JuliaComplexF64

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

elt: (%, Integer, Integer, JuliaComplexF64) -> JuliaComplexF64

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

empty?: % -> Boolean

from Aggregate

empty: () -> %

from Aggregate

enumerate: () -> List % if JuliaComplexF64 has Finite

from Finite

eq?: (%, %) -> Boolean

from Aggregate

eval: (%, Equation JuliaComplexF64) -> % if JuliaComplexF64 has Evalable JuliaComplexF64

from Evalable JuliaComplexF64

eval: (%, JuliaComplexF64, JuliaComplexF64) -> % if JuliaComplexF64 has Evalable JuliaComplexF64

from InnerEvalable(JuliaComplexF64, JuliaComplexF64)

eval: (%, List Equation JuliaComplexF64) -> % if JuliaComplexF64 has Evalable JuliaComplexF64

from Evalable JuliaComplexF64

eval: (%, List JuliaComplexF64, List JuliaComplexF64) -> % if JuliaComplexF64 has Evalable JuliaComplexF64

from InnerEvalable(JuliaComplexF64, JuliaComplexF64)

every?: (JuliaComplexF64 -> Boolean, %) -> Boolean

from HomogeneousAggregate JuliaComplexF64

exquo: (%, JuliaComplexF64) -> Union(%, failed)

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

hash: % -> SingleInteger if JuliaComplexF64 has Finite

from Hashable

hashUpdate!: (HashState, %) -> HashState if JuliaComplexF64 has Finite

from Hashable

index: PositiveInteger -> % if JuliaComplexF64 has Finite

from Finite

inverse: % -> Union(%, failed)

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

latex: % -> String

from SetCategory

leftPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

leftPower: (%, PositiveInteger) -> %

from Magma

leftRecip: % -> Union(%, failed)

from MagmaWithUnit

less?: (%, NonNegativeInteger) -> Boolean

from Aggregate

listOfLists: % -> List List JuliaComplexF64

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

lookup: % -> PositiveInteger if JuliaComplexF64 has Finite

from Finite

map: ((JuliaComplexF64, JuliaComplexF64) -> JuliaComplexF64, %, %) -> %

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

map: (JuliaComplexF64 -> JuliaComplexF64, %) -> %

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

matrix: List List JuliaComplexF64 -> %

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

max: % -> JuliaComplexF64 if JuliaComplexF64 has OrderedSet

from HomogeneousAggregate JuliaComplexF64

max: ((JuliaComplexF64, JuliaComplexF64) -> Boolean, %) -> JuliaComplexF64

from HomogeneousAggregate JuliaComplexF64

maxColIndex: % -> Integer

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

maxRowIndex: % -> Integer

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

member?: (JuliaComplexF64, %) -> Boolean

from HomogeneousAggregate JuliaComplexF64

members: % -> List JuliaComplexF64

from HomogeneousAggregate JuliaComplexF64

min: % -> JuliaComplexF64 if JuliaComplexF64 has OrderedSet

from HomogeneousAggregate JuliaComplexF64

minColIndex: % -> Integer

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

minordet: % -> JuliaComplexF64

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

minRowIndex: % -> Integer

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

more?: (%, NonNegativeInteger) -> Boolean

from Aggregate

ncols: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

nrows: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

nullity: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

nullSpace: % -> List JuliaComplexF64Vector

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

one?: % -> Boolean

from MagmaWithUnit

opposite?: (%, %) -> Boolean

from AbelianMonoid

parts: % -> List JuliaComplexF64

from HomogeneousAggregate JuliaComplexF64

Pfaffian: % -> JuliaComplexF64

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

plenaryPower: (%, PositiveInteger) -> %

from NonAssociativeAlgebra JuliaComplexF64

qcoerce: JuliaComplexF64Matrix -> %

qcoerce(m) coerces m to JuliaComplexF64SquareMatrix trusting that m is square.

qelt: (%, Integer, Integer) -> JuliaComplexF64

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

random: () -> % if JuliaComplexF64 has Finite

from Finite

rank: % -> NonNegativeInteger

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

recip: % -> Union(%, failed)

from MagmaWithUnit

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix Integer, vec: Vector Integer) if JuliaComplexF64 has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: (Matrix %, Vector %) -> Record(mat: Matrix JuliaComplexF64, vec: Vector JuliaComplexF64)

from LinearlyExplicitOver JuliaComplexF64

reducedSystem: Matrix % -> Matrix Integer if JuliaComplexF64 has LinearlyExplicitOver Integer

from LinearlyExplicitOver Integer

reducedSystem: Matrix % -> Matrix JuliaComplexF64

from LinearlyExplicitOver JuliaComplexF64

retract: % -> Fraction Integer

from RetractableTo Fraction Integer

retract: % -> Integer

from RetractableTo Integer

retract: % -> JuliaComplexF64

from RetractableTo JuliaComplexF64

retractIfCan: % -> Union(Fraction Integer, failed)

from RetractableTo Fraction Integer

retractIfCan: % -> Union(Integer, failed)

from RetractableTo Integer

retractIfCan: % -> Union(JuliaComplexF64, failed)

from RetractableTo JuliaComplexF64

rightPower: (%, NonNegativeInteger) -> %

from MagmaWithUnit

rightPower: (%, PositiveInteger) -> %

from Magma

rightRecip: % -> Union(%, failed)

from MagmaWithUnit

row: (%, Integer) -> JuliaComplexF64Vector

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

rowEchelon: % -> %

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

sample: %

from AbelianMonoid

scalarMatrix: JuliaComplexF64 -> %

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

size?: (%, NonNegativeInteger) -> Boolean

from Aggregate

size: () -> NonNegativeInteger if JuliaComplexF64 has Finite

from Finite

smaller?: (%, %) -> Boolean if JuliaComplexF64 has Finite

from Comparable

square?: % -> Boolean

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

squareMatrix: JuliaComplexF64Matrix -> %

squareMatrix(m) returns a copy of m as a JuliaComplexF64SquareMatrix.

subtractIfCan: (%, %) -> Union(%, failed)

from CancellationAbelianMonoid

symmetric?: % -> Boolean

from RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

trace: % -> JuliaComplexF64

from SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

zero?: % -> Boolean

from AbelianMonoid

AbelianGroup

AbelianMonoid

AbelianSemiGroup

Aggregate

Algebra JuliaComplexF64

BasicType

BiModule(%, %)

BiModule(JuliaComplexF64, JuliaComplexF64)

CancellationAbelianMonoid

CoercibleFrom Fraction Integer

CoercibleFrom Integer

CoercibleFrom JuliaComplexF64

CoercibleTo JuliaComplexF64Matrix

CoercibleTo OutputForm

Comparable if JuliaComplexF64 has Finite

ConvertibleTo InputForm if JuliaComplexF64 has Finite

ConvertibleTo String

DifferentialExtension JuliaComplexF64

DifferentialRing

Evalable JuliaComplexF64 if JuliaComplexF64 has Evalable JuliaComplexF64

Finite if JuliaComplexF64 has Finite

finiteAggregate

FullyLinearlyExplicitOver JuliaComplexF64

FullyRetractableTo JuliaComplexF64

Hashable if JuliaComplexF64 has Finite

HomogeneousAggregate JuliaComplexF64

InnerEvalable(JuliaComplexF64, JuliaComplexF64) if JuliaComplexF64 has Evalable JuliaComplexF64

JuliaType

LeftModule %

LeftModule JuliaComplexF64

LinearlyExplicitOver Integer if JuliaComplexF64 has LinearlyExplicitOver Integer

LinearlyExplicitOver JuliaComplexF64

Magma

MagmaWithUnit

Module JuliaComplexF64

Monoid

NonAssociativeAlgebra JuliaComplexF64

NonAssociativeRing

NonAssociativeRng

NonAssociativeSemiRing

NonAssociativeSemiRng

PartialDifferentialRing Symbol if JuliaComplexF64 has PartialDifferentialRing Symbol

RectangularMatrixCategory(n, n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

RetractableTo Fraction Integer

RetractableTo Integer

RetractableTo JuliaComplexF64

RightModule %

RightModule Integer if JuliaComplexF64 has LinearlyExplicitOver Integer

RightModule JuliaComplexF64

Ring

Rng

SemiGroup

SemiRing

SemiRng

SetCategory

SquareMatrixCategory(n, JuliaComplexF64, JuliaComplexF64Vector, JuliaComplexF64Vector)

TwoSidedRecip

unitsKnown