- 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
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 ]
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 ]
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 ]
Matrix == Matrix | 0 -> bool
Matrices can be compared for equality to another matrix
Zero is used as an alias for a zero matrix
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]])
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 ]
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 ]
Matrix.determinant() -> int | float
print(matrix.determinant())
# 0
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
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
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
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
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