pymatrices

pymatrices-0.1.0

A Python 3.x package to implement Matrices and almost all its Properties. It is also available on GitHub

Installation

Please Note :- Requires Python Version 3.x

If there are 2 or more versions of Python installed in your system (which mostly occurs in UNIX/Linux systems) then please run any one of the commands in the BASH/ZSH Shell :-

$ pip3 install pymatrices

$ python3 -m pip install pymatrices

If there is only Python 3.x installed in your system like in Windows systems then please run any one of commands in the Command Prompt :-

> pip install pymatrices

> python -m pip install pymatrices

Quick Guide :-

Please Read Till the End

Importing the Package :-

• Import the module by import pymatrices as pm.

Creating a Matrix and its Methods :-

• pm.matrix() creates a Matrix object.
  • It requires a 2-Dimensional List.
  • It stores it as a List, therefore it is mutable. To change the values, use <matrix object>[i][j] = value. Please Note that here i, j must be indices that obeys python's rules i.e '0' points to the 1st value.
• <matrix object>.asList() returns the List form of the matrix.
• <matrix object>.order returns the order of the matrix in a Tuple in the format of (rows, columns).
• <matrix object>.transpose returns the transpose of the matrix, which is another matrix object.
• All the Arithmetic Operations can be done by using their usual symbols.
  • However, two types of Multiplication can be done :-
    • <matrix.object>*(int or float) returns a Matrix with the int multiplied with each element of the matrix.
    • <matrix object>*<matrix object> returns a Matrix which is the product of the 2 matrices.
• <matrix object>.primaryDiagonal returns a List which has the Primany Diagonal Elements of the Matrix.
• <matrix object>.secondaryDiagonal returns a List which has the Secondary Diagonal Elements of the Matrix.
• <matrix object>.valueAt(row, column) returns the value at the given row and column. Please Note that here the row and column are normal indices and not python respective indices i.e '1' points to the first element. Refer Sample Implementation
• <matrix object>.minorOfValueAt(row, column) returns the matrix, which is the minor of the value at the given row and column.
• <matrix object>.position(value) returns a Tuple which are the indices of the given value; If the value is not found, it raises ValueError.

Uses of Additional Functions available in the Package :-

• pm.adjoint(<matrix>) returns the Adjoint Matrix (Adjugate Matrix) which is a matrix object.
• pm.createByFilling(value, order) returns a Matrix of given order and filled with the given value.
• pm.createColumnMatrix(values) returns a Column Matrix with the given values.
• pm.createRowMatrix(<matrix>) returns a Row Matrix with the given values.
• pm.determinant(<matrix>) returns the Determinant of the given matrix.
• pm.eigenvalues(<matrix>) returns the Eigenvalues of the matrix in a List.
• pm.eigenvectors(<matrix>) generates the corresponding Eigenvectors of the matrix in the order of the Eigenvalues.
• pm.inverse(<matrix>) returns the Inverse of the matrix, which is another matrix object.
• pm.I(order) returns the Identity matrix of the given order.
• pm.isDiagonal(<matrix>) returns True if the given matrix is a Diagonal Matrix else returns False.
• pm.isIdempotent(<matrix>) returns True if the given matrix is an Idempotent Matrix else returns False.
• pm.isIdentity(<matrix>) returns True if the given matrix is an Identity Matrix else returns False.
• pm.isInvolutory(<matrix>) returns True if the given matrix is an Involutory Matrix else returns False.
• pm.isNilpotent(<matrix>) returns True if the given matrix is a Nilpotent Matrix else returns False.
• pm.isNull(<matrix>) returns True if the given matrix is a Null Matrix else returns False.
• pm.isScalar(<matrix>) returns True if the given matrix is a Scalar Matrix else returns False.
• pm.isSingular(<matrix>) returns True if the given matrix is a Singular Matrix else returns False.
• pm.isSquare(<matrix>) returns True if the given matrix is a Square Matrix else returns False.
• pm.isSymmetric(<matrix>) returns True if the given matrix is a Symmetric Matrix else returns False.
• pm.isSkewSymmetric(<matrix>) returns True if the given matrix is a Skew Symmetric Matrix else returns False.
• pm.O(order) returns the Square Null matrix of the given order.

A Sample Implementation :-

Just Run the Script in your IDE after installing the package

import pymatrices as pm

M1 = pm.matrix([[1,2,1],[4,5,6],[7,8,9]])
M2 = pm.matrix([[-5,2],[-9,6]])
M3 = pm.I(3)

print("M1 :\n", M1, sep="")
print("M2 :\n", M2, sep="")
print("M3 :\n", M3, sep="")

M1[0][0] = 2
print("After changing a value of M1 :\n", M1, sep="")

print(f"Matrix in List Form : {M1.asList()}")

print("Transpose of M1 :\n", M1.transpose, sep="")
print("Transpose of M2 :\n", M2.transpose, sep="")
print("Transpose of M3 :\n", M3.transpose, sep="")

print("M1+M3 :\n", M1+M3, sep="")
print("M1-M3 :\n", M1-M3, sep="")

print("M1*M3 :\n", M1*M3, sep="")
print("M1*3 :\n", M3*3, sep="")

print("\nPrimary Diagonal Values of M1 :", M1.primaryDiagonal)
print("Primary Diagonal Values of M2 :", M2.primaryDiagonal)

print("\nSecondary Diagonal Values of M1 :", M1.secondaryDiagonal)
print("Secondary Diagonal Values of M2 :", M2.secondaryDiagonal)

print("\nM1[1][1] :", M1.valueAt(1, 1))
print("M1[1][2] :", M1.valueAt(1, 2))

print("\nMinor of 1 in M1:\n", M1.minorOfValueAt(1, 1), sep="")
print("Minor of 2 in M1 :\n", M1.minorOfValueAt(2, 2), sep="")

print("Index of 1 in M1 :", M1.position(1))
print("Index of 8 in M1 :", M1.position(8))

print("\nadj M1 :\n", pm.adjoint(M1), sep="")
print("adj M2 :\n", pm.adjoint(M2), sep="")

print("Matrix created by Filling a particular value :\n", pm.createByFilling(2, (2, 3)), sep="")

print("A Sample Column Matrix :\n", pm.createColumnMatrix([2,3,4,5]), sep="")

print("A Sample Row Matrix :\n", pm.createRowMatrix([2,3,4,5]), sep="")

print("|M1| :", pm.determinant(M1))
print("|M2| :", pm.determinant(M2))

print("\nEigenvalues of M1 :", pm.eigenvalues(M1))
print("\nCorresponding Eigenvectors of M1:-")
for _ in pm.eigenvectors(M1):
	print(_)

print("Eigenvalues of M2 :", pm.eigenvalues(M2))
print("\nCorresponding Eigenvectors of M2:-")
for _ in pm.eigenvectors(M2):
	print(_)

print("Inverse of M1 :\n", pm.inverse(M1), sep="")
print("Inverse of M2 :\n", pm.inverse(M2), sep="")

print("A 3x3 Identity Matrix :\n", pm.I(3), sep="")
print("A 3x3 Null Matrix :\n", pm.O(3), sep="")

print("Is M1 a Diagonal Matrix? ", pm.isDiagonal(M1), sep="")
print("Is M1 an Identity Matrix? ", pm.isIdentity(M1), sep="")

print("\nIs M1 an Idempotent Matrix? ", pm.isIdempotent(M1), sep="")
print("Is a 3x3 Identity Matrix an Idempotent Matrix? ", pm.isIdempotent(pm.I(3)), sep="")

print("\nIs M1 an Involutory Matrix? ", pm.isInvolutory(M1), sep="")
print("Is a 3x3 Identity Matrix an Involutory Matrix? ", pm.isInvolutory(pm.I(3)), sep="")

print("\nIs M1 a Nilpotent Matrix? ", pm.isNilpotent(M1), sep="")

print("\nIs M1 a Null Matrix? ", pm.isNull(M1), sep="")
print("Is a 3x3 Null Matrix, a Null Matrix? ", pm.isNull(pm.O(3)), sep="")

print("\nIs M1 a Scalar Matrix? ", pm.isScalar(M1), sep="")
print("Is M1 a Singular Matrix? ", pm.isSingular(M1), sep="")
print("Is M1 a Square Matrix? ", pm.isSquare(M1), sep="")
print("Is M1 a Symmetric Matrix? ", pm.isSymmetric(M1), sep="")
print("Is M1 a Skew Symmetric Matrix? ", pm.isSkewSymmetric(M1), sep="")