mathmatrix 0.5
A package for Python that lets you create and perform various operations on Matrices sucjh as finding the adjoint, inverse, determinant of a matrix, etc..
License: MIT
Keywords: matrix,math,mathmatrix,matrices,matrix inverse,determinant

Features
~~~~~~~~

-  Addition, Multiplication, Division, Subraction operations supported
   between matrices and between a matrix and a int / float
-  Calculates:

   -  Determinant
   -  Inverse
   -  Cofactor of a given element in the Matrix
   -  Adjoint

Getting started
---------------

Creating a Matrix
^^^^^^^^^^^^^^^^^

To create a matrix, specify the order of the Matrix (mxn) where the
first argument (m) is the number of rows in the matrix and the second
argument (n) is the number of columns

We can use a nested list to represent a Matrix during initialization of
an object In a nested list, the length of the outer list would be ‘m’
and the number of elements the inner lists have would be ‘n’

.. code:: python

   from matrix import Matrix

   matrix_list = [
       [1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]
   ]

   matrix1 = Matrix(3, 3, matrix_list)

   print(matrix1)
   #Prints:
   # [ 1, 2, 3
   #   4, 5, 6
   #   7, 8, 9 ]

Operations on Matrices
======================

Addition and Subraction
~~~~~~~~~~~~~~~~~~~~~~~

We can add and subract matrices extremely easily:

.. code:: python

   matrix_list2 = [
       [0, 1, 3], 
       [5, 2, 7], 
       [7, 1, 9]
   ]
   matrix2 = Matrix(3, 3, matrix_list2)
   matrix3 = matrix1 + matrix2
   print(matrix3)
   #Prints:
   # [ 1, 3, 6
   #   9, 7, 13
   #   14, 9, 18 ]

Adding an int / float to a matrix will perform the operation on all
elements of the matrix and return a new matrix

.. code:: python

   matrix4 = matrix1 + 5
   print(matrix4)
   #Prints:
   # [ 6, 7, 8
   #   9, 10, 11
   #   12, 13, 14 ]
   # Same way,
   print(matrix4 - matrix1)
   # [ 5, 5, 5
   #   5, 5, 5
   #   5, 5, 5 ]
   print(matrix1 - 3)
   #Prints:
   # [ -2, -1, 0
   #   1, 2, 3
   #   4, 5, 6 ]

Multiplication and Division
~~~~~~~~~~~~~~~~~~~~~~~~~~~

Matrix multiplication can only be implemented if the number of columns
in the first matrix is equal to the number of rows in the other matrix.
Basically: A ``m x n`` Matrix can only be multiplied with a ``n x l``
Matrix .

The order of the resultant Matrix will be ``m x l``

Example:

.. code:: python

   # m x n * n x l : Gives m x l
   # 2 x 3 * 3 x 2 : Gives 2 x 2
   # 2 x 3 * 4 x 2 : Cannot mutliply

Internally, division is calculated by multiplying a matrix and the
inverse of the other matrix therefore the same condition applies for
division

.. code:: python

   print(matrix1 * 5)
   # [ 5, 10, 15
   #   20, 25, 30
   #   35, 40, 45 ]
   print(matrix1 * matrix2)
   # [ 31, 8, 44
   #   67, 20, 101
   #   103, 32, 44 ]

Comparing matrices
~~~~~~~~~~~~~~~~~~

``Matrix == Matrix | 0 -> bool``

Matrices can be compared for equality to another matrix Zero is used as
an alias for a zero matrix

Functionalities
---------------

``mathmatrix`` provides many functionalities for matrices out of the
box:

Let’s create a sample matrix ``matrix`` to perform the operations on

.. code:: python

   from mathmatrix import Matrix

   matrix = Matrix(3,3,[[1,2,3],[4,5,6],[7,8,9]])

Transposing a matrix
~~~~~~~~~~~~~~~~~~~~

``Matrix.transpose() -> Matrix``

After creating a matrix, you can transpose a Matrix using the
``transpose()`` method of Matrix

.. code:: python

   print(matrix.transpose())
   # [ 1, 4, 7
   #   2, 5, 8
   #   3, 6, 7 ]

Adjoint of a Matrix
~~~~~~~~~~~~~~~~~~~

``Matrix.adjoint() -> Matrix``

Adjoint of a matrix is calculated as the transpose of cofactor matrix of
a Matrix It can be calculated using the ``adjoint()`` method

.. code:: python

   print(matrix.adjoint())
   # [ -3, 6, -3
   #   6, -12, 6
   #  -3, 6, -3 ]

Determinant of a Matrix
~~~~~~~~~~~~~~~~~~~~~~~

``Matrix.determinant() -> int | float``

.. code:: python

   print(matrix.determinant())
   # 0

Inverse of a Matrix
~~~~~~~~~~~~~~~~~~~

``Matrix.inverse() -> Matrix``

Inverse of a matrix only exists for non-singular matrices ( Determinant
of the Matrix should not be zero )

.. code:: python

   print(matrix.determinant())
   # 0
   # Since determinant is zero, if we try to calculate Inverse it will throw the error:
   # ZeroDivisionError: Determinant of Matrix is zero, inverse of the matrix does not exist

Cofactor of an element
~~~~~~~~~~~~~~~~~~~~~~

``Matrix.cofactor(m:int, n:int) -> int | float``

Specify the position of the desired element in row number (m) and column
number (n) to calculate it’s corresponding cofactor

Chaining functions
~~~~~~~~~~~~~~~~~~

Since functions return a new Matrix, you can chain many functions to get
the desired output For example:

.. code:: python

   matrix.transpose().adjoint().determinant()
   (matrix.determinant() * matrix.adjoint()).transpose()

are all completely valid

Additional Functions
--------------------

Generating a zero matrix
~~~~~~~~~~~~~~~~~~~~~~~~

``gen_zero_matrix(m:int, n:int) -> Matrix``

You can use the ``gen_zero_matrix`` function to create a zero matrix of
a given order For example,

.. code:: python

   from mathmatrix import gen_zero_matrix, Matrix
   zero3 = gen_zero_matrix(3,3) 
   print(zero3)
   # [ 0, 0, 0
   #   0, 0, 0
   #   0, 0, 0 ]
   print(zero3 == 0)
   # True

Generating an identity matrix
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

``gen_zero_matrix(m:int, n:int) -> Matrix``

You can use the ``gen_zero_matrix`` function to create a zero matrix of
a given order For example,

.. code:: python

   from mathmatrix import gen_zero_matrix, Matrix
   zero3 = gen_zero_matrix(3,3) 
   print(zero3)
   # [ 0, 0, 0
   #   0, 0, 0
   #   0, 0, 0 ]
   print(zero3 == 0)
   # True

Note: For any Matrix ``matrix``,

.. code:: python

   print(matrix * matrix.inverse() == gen_identity_matrix(matrix.m, matrix.n))
   # Always true (Inverse cannot be calculated for singular matrices so error is thrown in that case)
   print((matrix - matrix) == gen_zero_matrix(matrix.m,matrix.n))
   # Always true