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'

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:

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

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:

# 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

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

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

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

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

Determinant of a Matrix

Matrix.determinant() -> int | float

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 )

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:

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,

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,

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,

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