NormalMatrix

A module for Normal Matrix

Types

type NormalMatrix a

= NormalMatrix (SquareMatrix a)

Symmetric Matrix type

Constructors

createMatrixFromColumnVectors : List (ColumnVector a) -> NormalMatrix a

Create a Matrix from a list of Column Vectors

identity : Field a -> Int -> NormalMatrix a

Create Square Identity Matrix with n dimension

Matrix Predicates and Properties

dimension : NormalMatrix a -> Int

Dimension of the matrix

isNormalMatrix : InnerProductSpace a -> SquareMatrix a -> Bool

Predicate to determine if Matrix is normal

getDiagonalProduct : Field a -> NormalMatrix a -> Maybe a

Get the Product of the diagonal of a Matrix

subMatrix : Int -> Int -> Int -> Int -> NormalMatrix a -> NormalMatrix a

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

transpose : NormalMatrix a -> NormalMatrix a

Transpose a Matrix

Unitary Operations

scalarMultiplication : Field a -> a -> NormalMatrix a -> NormalMatrix a

Scalar multiplication over a Square Matrix

adjoint :

NormalMatrix (ComplexNumber number)

-> NormalMatrix (ComplexNumber number)

Perform the adjoint operation on a Complex Numbered Matrix

Binary Operations

add : Field a -> NormalMatrix a -> NormalMatrix a -> NormalMatrix a

Add two NormalMatrix together

multiply :

InnerProductSpace a

-> NormalMatrix a

-> Result String (NormalMatrix a)

Square Matrix Square Matrix multiplication

multiplyMatrixVector :

InnerProductSpace a

-> NormalMatrix a

-> ColumnVector a

-> Result String (ColumnVector a)

Multiply a Vector by a Matrix

subtract : Field a -> NormalMatrix a -> NormalMatrix a -> NormalMatrix a

Subtract two Square Matrices

Manipulation

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

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

Monoid

appendHorizontal : NormalMatrix a -> NormalMatrix a -> NormalMatrix a

Append Matricies together horizontally

Equality

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

Compare two matricies using comparator

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

Compare two Matrices for equality

Matrix Forms

gaussJordan : VectorSpace a -> NormalMatrix a -> NormalMatrix a

Function composition of Gaussian Elimination and Jordan Elimination

upperTriangle : VectorSpace a -> NormalMatrix a -> NormalMatrix a

Put a matrix into Upper Triangular Form

jonathanfishbein1/linear-algebra/25.2.0