SquareMatrix

A module for Square Matrix

Types

type SquareMatrix a

= SquareMatrix (Matrix a)

Square Matrix type

type alias InnerProductSpace a =

{ matrixSpace : MatrixSpace a

, innerProduct : SquareMatrix a -> SquareMatrix a -> Result String a

, norm : SquareMatrix a -> Result String (Real Float)

, distance :

SquareMatrix a -> SquareMatrix a -> Result String (Real Float)

}

Type to represent an Inner Product Space

Values

zeroSquareMatrix : Field a -> Int -> SquareMatrix a

Create square Matrix with n dimension filled with zeros

realMatrixInnerProductSpace : InnerProductSpace (Real Float)

Real Numbered Inner Product Space for Matrix

complexMatrixInnerProductSpace : InnerProductSpace (ComplexNumber Float)

Complex Numbered Inner Product Space for Matrix

Constructors

createMatrixFromColumnVectors : List (ColumnVector a) -> SquareMatrix a

Create a Matrix from a list of Column Vectors

identity : Field a -> Int -> SquareMatrix a

Create Square Identity Matrix with n dimension

Matrix Predicates and Properties

dimension : SquareMatrix a -> Int

Dimension of the matrix

isSquareMatrix : Matrix a -> Bool

Determine whether a matirx is square

normReal : SquareMatrix (Real Float) -> Result String (Real Float)

Calculate the norm of a Matrix

normComplex : SquareMatrix (ComplexNumber Float) -> Result String (Real Float)

Calculate the norm of a Matrix

distanceReal :

SquareMatrix (Real Float)

-> SquareMatrix (Real Float)

-> Result String (Real Float)

Calculate distance between two vectors

isRightStochastic : SquareMatrix (Real Float) -> Bool

Predicate if matrix is right stochastic

isLeftStochastic : SquareMatrix (Real Float) -> Bool

Predicate if matrix is left stochastic

getDiagonalProduct : Field a -> SquareMatrix a -> Maybe a

Get the Product of the diagonal of a Matrix

subMatrix : Int -> Int -> Int -> Int -> SquareMatrix a -> SquareMatrix a

Calculate the submatrix given a starting and ending row and column index

transpose : SquareMatrix a -> SquareMatrix a

Transpose a Matrix

Unitary Operations

scalarMultiplication : Field a -> a -> SquareMatrix a -> SquareMatrix a

Scalar multiplication over a Square Matrix

adjoint :

SquareMatrix (ComplexNumber number)

-> SquareMatrix (ComplexNumber number)

Perform the adjoint operation on a Complex Numbered Matrix

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

Map over a Matrix

Binary Operations

dotProduct :

InnerProductSpace a

-> SquareMatrix a

-> Result String a

Calculate the dot product of two Matricies

multiply :

InnerProductSpace a

-> SquareMatrix a

-> Result String (SquareMatrix a)

Square Matrix Square Matrix multiplication

multiplyMatrixVector :

InnerProductSpace a

-> SquareMatrix a

-> ColumnVector a

-> Result String (ColumnVector a)

Multiply a Vector by a Matrix

add : Field a -> SquareMatrix a -> SquareMatrix a -> SquareMatrix a

Add two Square Matrices together

subtract : Field a -> SquareMatrix a -> SquareMatrix a -> SquareMatrix a

Subtract two Square Matrices

Manipulation

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

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

Monoid

appendHorizontal : SquareMatrix a -> SquareMatrix a -> SquareMatrix a

Append Matricies together horizontally

Equality

equal : (a -> a -> Bool) -> Equality (SquareMatrix a)

Compare two matricies using comparator

equalImplementation : (a -> a -> Bool) -> SquareMatrix a -> SquareMatrix a -> Bool

Compare two Matrices for equality

Matrix Forms

gaussJordan : VectorSpace a -> SquareMatrix a -> SquareMatrix a

Function composition of Gaussian Elimination and Jordan Elimination

upperTriangle : VectorSpace a -> SquareMatrix a -> SquareMatrix a

Put a matrix into Upper Triangular Form

jonathanfishbein1/linear-algebra/26.0.0

SquareMatrix

Types

Values

Constructors

Matrix Predicates and Properties

Unitary Operations

Binary Operations

Manipulation

Monoid

Equality

Matrix Forms

Modules