Math.LinearMap.Category

Linear maps

Function implementation

data LinearFunction s v w

type v -+> w

type Bilinear v w y

lfun

Tensor implementation

data LinearMap s v w

type v +> w

(⊕)

(>+<)

adjoint

Dual vectors

(<.>^)

(-+|>)

Tensor spaces

data Tensor s v w

type v w

(⊗)

Symmetric

data SymmetricTensor s v

squareV

squareVs

type ⊗〃+> v w

currySymBilin

Norms

data Norm v

type Seminorm v

spanNorm

euclideanNorm

(|$|)

normSq

(<$|)

scaleNorm

normSpanningSystem

normSpanningSystem'

Variances

type Variance v

spanVariance

(|&>)

varianceSpanningSystem

dualNorm

dualNorm'

dependence

Utility

densifyNorm

wellDefinedNorm

Solving linear equations

(\$)

pseudoInverse

roughDet

linearRegressionW

linearRegressionWVar

Eigenvalue problems

eigen

constructEigenSystem

roughEigenSystem

finishEigenSystem

data Eigenvector v

The classes of suitable vector spaces

type LSpace v

class TensorSpace v

class LinearSpace v

Orthonormal systems

class SemiInner v

cartesianDualBasisCandidates

embedFreeSubspace

Finite baseis

class FiniteDimensional v

Utility

Linear primitives

addV

scale

inner

flipBilin

bilinearFunction

Tensors with basis decomposition

(.⊗)

Hilbert space operations

type DualSpace v

riesz

coRiesz

showsPrecAsRiesz

(.<)

Constraint synonyms

type HilbertSpace v

type SimpleSpace v

class Num' s

type Fractional' s

type RealFrac' s

type RealFloat' s

type LinearShowable v

Double-dual, scalar-scalar etc. identity

data ClosedScalarWitness s

data ScalarSpaceWitness v

data DualSpaceWitness v

data LinearManifoldWitness v

Misc

relaxNorm

transformNorm

transformVariance

findNormalLength

normalLength

summandSpaceNorms

sumSubspaceNorms

sharedNormSpanningSystem

sharedSeminormSpanningSystem

sharedSeminormSpanningSystem'

convexPolytopeHull

convexPolytopeRepresentatives