Matrix

A module for Matrix

Types

type Matrix a

= Matrix (List (RowVector a))

Matrix type

type RowVector a

= RowVector (Vector a)

Row Vector

type ColumnVector a

= ColumnVector (Vector a)

Column Vector

type Solution

= UniqueSolution (ColumnVector Float)

| InfiniteSolutions

{ nullity : Int

, rank : Int

}

| NoUniqueSolution String

Type to represent result of Gauss-Jordan reduction

type VectorSpace

= VectorSpace Int

Type to represent vector space such as R, R2, R3

addRealMatrices : Matrix number -> Matrix number -> Matrix number

Add two Real Matrices together

addComplexMatrices :

Matrix (ComplexNumberCartesian number)

-> Matrix (ComplexNumberCartesian number)

Add two Complex Matrices together

sumRealMatrices : Matrix number -> Monoid (Matrix number)

Monoidally add two Real numbered Matrices together

sumComplexMatrices :

Matrix (ComplexNumberCartesian number)

-> Monoid (Matrix (ComplexNumberCartesian number))

Monoidally add two Complex numbered Matrices together

map : (a -> b) -> Matrix a -> Matrix b

Map over a Matrix

equal : (a -> a -> Bool) -> Matrix a -> Matrix a -> Bool

Compare two matricies using comparator

transpose : Matrix a -> Matrix a

Transpose a Matrix

conjugate :

Matrix (ComplexNumberCartesian number)

-> Matrix (ComplexNumberCartesian number)

Take the complex conjugate of a Complex Numbered Matrix

adjoint :

Matrix (ComplexNumberCartesian number)

-> Matrix (ComplexNumberCartesian number)

Perform the adjoint operation on a Complex Numbered Matrix

apply : Matrix (a -> b) -> Matrix a -> Matrix b

Apply for Matrix

liftA2 : (a -> b -> c) -> Matrix a -> Matrix b -> Matrix c

Lift a function to work on Matrix

multiplyComplexMatrices :

Matrix (ComplexNumberCartesian number)

-> Matrix (ComplexNumberCartesian number)

-> Result String (Matrix (ComplexNumberCartesian number))

Matrix Matrix multiplication for a Complex Numbered Matrix

multiplyRealMatrices : Matrix number -> Matrix number -> Result String (Matrix number)

Matrix Matrix multiplication for a Real Numbered Matrix

identityMatrix : Int -> Matrix Int

Create Identity Matrix with n dimension

gaussJordan : Matrix Float -> Matrix Float

Function composition of Gaussian Elimination and Jordan Elimination

gaussianReduce : Matrix Float -> Matrix Float

Gaussian Elimination

isHermitian : Matrix (ComplexNumberCartesian number) -> Bool

Predicate to determine if Matrix is Hermitian

isSymmetric : Matrix a -> Bool

Predicate to determine if Matrix is symmetric

jordanReduce : Matrix Float -> Matrix Float

Internal function for Jordan Elimination

areLinearlyIndependent : List (RowVector Float) -> Bool

Predicate to determine if a list of Vectors are linearly independent

multiplyRealVectorRealMatrix : Matrix number -> Vector number -> Vector number

Multiply a real Vector by a real Matrix

nullSpace : Matrix Float -> Solution

Calculate the null space of a matrix

solve : Matrix Float -> ColumnVector Float -> Solution

Solve a system of linear equations using Gauss-Jordan elimination with explict augmented side column vector

areBasis : VectorSpace -> List (RowVector Float) -> Bool

Determine whether list of vectors are a basis for a space

basisOfVectorSpace : VectorSpace -> List (RowVector Float) -> List (RowVector Float)

Determine the basis vectors of a vector space

doesSetSpanSpace : VectorSpace -> List (RowVector Float) -> Result String Bool

Determine whether list of vectors spans a space

mDimension : Matrix a -> Int

Number of rows in Matrix

nDimension : Matrix a -> Int

Number of columns in Matrix

solveMatrix : Matrix Float -> Solution

Solve a system of linear equations using Gauss-Jordan elimination

foldl : (a -> b -> b) -> b -> Matrix a -> b

Left fold over a Matrix

matrixConcatHorizontal : Monoid (Matrix a)

Monoidally append Matricies together horizontally

matrixConcatVertical : Monoid (Matrix a)

Monoidally append Matricies together vertically

matrixEmpty : Matrix a

Monoid empty for Vector

pure : a -> Matrix a

Applicative pure for Matrix

bind : Matrix a -> (a -> Matrix b) -> Matrix b

Monad bind for Matrix

determinant : Matrix Float -> Maybe Float

Try to calculate the determinant

getAt : ( Int, Int ) -> Matrix a -> Maybe a

Get the value in a matrix at the specified row and column

print : Matrix Float -> String

Print a matrix to a string

read : String -> Result (List DeadEnd) (Matrix Float)

Try to read a string into a Matrix

setAt : ( Int, Int ) -> a -> Matrix a -> Matrix a

Set the value in a Matrix at the specified row and column

upperTriangle : Matrix Float -> Matrix Float

Put a matrix into Upper Triangular Form

jonathanfishbein1/linear-algebra/5.1.0

Matrix

Types

Modules