Matrix(R)

matrix.spad line 69 [edit on github]

• R : AbelianMonoid

Matrix is a matrix domain where 1-based indexing is used for both rows and columns.

# : % -> NonNegativeInteger

from Aggregate

* : (%, %) -> % if R has SemiRng

from MatrixCategory(R, Vector(R), Vector(R))

* : (%, R) -> % if R has SemiRng

from MatrixCategory(R, Vector(R), Vector(R))

* : (R, %) -> % if R has SemiRng

from MatrixCategory(R, Vector(R), Vector(R))

* : (Integer, %) -> % if R has AbelianGroup

from MatrixCategory(R, Vector(R), Vector(R))

* : (%, Vector(R)) -> Vector(R) if R has SemiRng

from MatrixCategory(R, Vector(R), Vector(R))

* : (Vector(R), %) -> Vector(R) if R has SemiRng

from MatrixCategory(R, Vector(R), Vector(R))

+ : (%, %) -> %

from MatrixCategory(R, Vector(R), Vector(R))

- : % -> % if R has AbelianGroup

from MatrixCategory(R, Vector(R), Vector(R))

- : (%, %) -> % if R has AbelianGroup

from MatrixCategory(R, Vector(R), Vector(R))

/ : (%, R) -> % if R has Field

from MatrixCategory(R, Vector(R), Vector(R))

= : (%, %) -> Boolean

from BasicType

Pfaffian : % -> R if R has CommutativeRing

from MatrixCategory(R, Vector(R), Vector(R))

^ : (%, Integer) -> % if R has Field

from MatrixCategory(R, Vector(R), Vector(R))

^ : (%, NonNegativeInteger) -> % if R has Monoid and R has SemiRng

from MatrixCategory(R, Vector(R), Vector(R))

antisymmetric? : % -> Boolean if R has AbelianGroup

from MatrixCategory(R, Vector(R), Vector(R))

any? : (Mapping(Boolean, R), %) -> Boolean

from HomogeneousAggregate(R)

array2 : List(List(R)) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

blockConcat : List(List(%)) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

blockSplit : (%, List(NonNegativeInteger), List(NonNegativeInteger)) -> List(List(%))

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

blockSplit : (%, PositiveInteger, PositiveInteger) -> List(List(%))

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

coerce : Vector(R) -> %

from MatrixCategory(R, Vector(R), Vector(R))

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

colSlice : % -> Segment(Integer)

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

column : (%, Integer) -> Vector(R)

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

columnSpace : % -> List(Vector(R)) if R has EuclideanDomain

from MatrixCategory(R, Vector(R), Vector(R))

convert : % -> InputForm if R has ConvertibleTo(InputForm)

from ConvertibleTo(InputForm)

copy : % -> %

from Aggregate

count : (R, %) -> NonNegativeInteger

from HomogeneousAggregate(R)

count : (Mapping(Boolean, R), %) -> NonNegativeInteger

from HomogeneousAggregate(R)

determinant : % -> R if R has CommutativeRing

from MatrixCategory(R, Vector(R), Vector(R))

diagonal? : % -> Boolean

from MatrixCategory(R, Vector(R), Vector(R))

diagonalMatrix : List(%) -> %

from MatrixCategory(R, Vector(R), Vector(R))

diagonalMatrix : List(R) -> %

from MatrixCategory(R, Vector(R), Vector(R))

diagonalMatrix : Vector(R) -> %

diagonalMatrix(v) returns a diagonal matrix where the elements of v appear on the diagonal.

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

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

elt : (%, Integer, List(Segment(Integer))) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

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

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

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

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

elt : (%, List(Integer), Segment(Integer)) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

elt : (%, List(Segment(Integer)), Integer) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

elt : (%, List(Segment(Integer)), List(Segment(Integer))) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

elt : (%, List(Segment(Integer)), Segment(Integer)) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

elt : (%, Segment(Integer), List(Integer)) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

elt : (%, Segment(Integer), List(Segment(Integer))) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

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

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

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

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

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

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

empty : () -> %

from Aggregate

empty? : % -> Boolean

from Aggregate

eq? : (%, %) -> Boolean

from Aggregate

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

from InnerEvalable(R, R)

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

from Evalable(R)

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

from InnerEvalable(R, R)

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

from Evalable(R)

every? : (Mapping(Boolean, R), %) -> Boolean

from HomogeneousAggregate(R)

exquo : (%, R) -> Union(%, "failed") if R has IntegralDomain

from MatrixCategory(R, Vector(R), Vector(R))

fill! : (%, R) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

hash : % -> SingleInteger if R has Hashable

from Hashable

hashUpdate! : (HashState, %) -> HashState if R has Hashable

from Hashable

horizConcat : (%, %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

horizConcat : List(%) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

horizSplit : (%, List(NonNegativeInteger)) -> List(%)

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

horizSplit : (%, PositiveInteger) -> List(%)

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

inverse : % -> Union(%, "failed") if R has Field

from MatrixCategory(R, Vector(R), Vector(R))

invertIfCan : % -> Union(%, "failed") if R has IntegralDomain

invertIfCan(m) returns the inverse of the matrix m. If the matrix is not invertible, "failed" is returned. Error: if the matrix is not square.

kroneckerProduct : (%, %) -> % if R has SemiRng

from MatrixCategory(R, Vector(R), Vector(R))

kroneckerProduct : List(%) -> % if R has SemiRng

from MatrixCategory(R, Vector(R), Vector(R))

kroneckerSum : (%, %) -> %

from MatrixCategory(R, Vector(R), Vector(R))

kroneckerSum : List(%) -> %

from MatrixCategory(R, Vector(R), Vector(R))

kronecker_prod1 : (%, Integer, List(List(NonNegativeInteger)), List(%), NonNegativeInteger, NonNegativeInteger, Union(R, "one")) -> Void

from MatrixCategory(R, Vector(R), Vector(R))

latex : % -> String

from SetCategory

less? : (%, NonNegativeInteger) -> Boolean

from Aggregate

listOfLists : % -> List(List(R))

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

map : (Mapping(R, R), %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

map : (Mapping(R, R, R), %, %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

map : (Mapping(R, R, R), %, %, R) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

map! : (Mapping(R, R), %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

matrix : List(List(R)) -> %

from MatrixCategory(R, Vector(R), Vector(R))

matrix : (NonNegativeInteger, NonNegativeInteger, Mapping(R, Integer, Integer)) -> %

from MatrixCategory(R, Vector(R), Vector(R))

max : % -> R if R has OrderedSet

from HomogeneousAggregate(R)

max : (Mapping(Boolean, R, R), %) -> R

from HomogeneousAggregate(R)

maxColIndex : % -> Integer

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

maxRowIndex : % -> Integer

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

member? : (R, %) -> Boolean

from HomogeneousAggregate(R)

members : % -> List(R)

from HomogeneousAggregate(R)

min : % -> R if R has OrderedSet

from HomogeneousAggregate(R)

minColIndex : % -> Integer

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

minRowIndex : % -> Integer

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

minordet : % -> R if R has CommutativeRing

from MatrixCategory(R, Vector(R), Vector(R))

more? : (%, NonNegativeInteger) -> Boolean

from Aggregate

ncols : % -> NonNegativeInteger

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

new : (NonNegativeInteger, NonNegativeInteger, R) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

nrows : % -> NonNegativeInteger

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

nullSpace : % -> List(Vector(R)) if R has IntegralDomain

from MatrixCategory(R, Vector(R), Vector(R))

nullity : % -> NonNegativeInteger if R has IntegralDomain

from MatrixCategory(R, Vector(R), Vector(R))

parts : % -> List(R)

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

positivePower : (%, Integer) -> % if R has SemiRng

from MatrixCategory(R, Vector(R), Vector(R))

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

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

qnew : (NonNegativeInteger, NonNegativeInteger) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

qsetelt! : (%, Integer, Integer, R) -> R

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

rank : % -> NonNegativeInteger if R has IntegralDomain

from MatrixCategory(R, Vector(R), Vector(R))

row : (%, Integer) -> Vector(R)

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

rowEchelon : % -> % if R has EuclideanDomain

from MatrixCategory(R, Vector(R), Vector(R))

rowSlice : % -> Segment(Integer)

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

sample : () -> %

from Aggregate

scalarMatrix : (NonNegativeInteger, R) -> %

from MatrixCategory(R, Vector(R), Vector(R))

setColumn! : (%, Integer, Vector(R)) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setRow! : (%, Integer, Vector(R)) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, Integer, List(Integer), %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, Integer, List(Segment(Integer)), %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, List(Integer), Integer, %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, List(Integer), List(Integer), %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, List(Integer), Segment(Integer), %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, List(Segment(Integer)), Integer, %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, List(Segment(Integer)), List(Segment(Integer)), %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, List(Segment(Integer)), Segment(Integer), %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, Segment(Integer), List(Integer), %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, Segment(Integer), List(Segment(Integer)), %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, Segment(Integer), Segment(Integer), %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setelt! : (%, Integer, Integer, R) -> R

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

setsubMatrix! : (%, Integer, Integer, %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

size? : (%, NonNegativeInteger) -> Boolean

from Aggregate

smaller? : (%, %) -> Boolean if R has Comparable

from Comparable

square? : % -> Boolean

from MatrixCategory(R, Vector(R), Vector(R))

squareTop : % -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

subMatrix : (%, Integer, Integer, Integer, Integer) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

swapColumns! : (%, Integer, Integer) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

swapRows! : (%, Integer, Integer) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

symmetric? : % -> Boolean

from MatrixCategory(R, Vector(R), Vector(R))

transpose : % -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

transpose : Vector(R) -> %

from MatrixCategory(R, Vector(R), Vector(R))

vertConcat : (%, %) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

vertConcat : List(%) -> %

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

vertSplit : (%, List(NonNegativeInteger)) -> List(%)

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

vertSplit : (%, PositiveInteger) -> List(%)

from TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

zero : (NonNegativeInteger, NonNegativeInteger) -> %

from MatrixCategory(R, Vector(R), Vector(R))

zero? : % -> Boolean

from MatrixCategory(R, Vector(R), Vector(R))

~= : (%, %) -> Boolean

from BasicType

Comparable

ConvertibleTo(InputForm)

shallowlyMutable

HomogeneousAggregate(R)

Aggregate

BasicType

MatrixCategory(R, Vector(R), Vector(R))

TwoDimensionalArrayCategory(R, Vector(R), Vector(R))

SetCategory

InnerEvalable(R, R)

CoercibleTo(OutputForm)

Hashable

finiteAggregate

Evalable(R)