This is my database of projects that supported me alot during classes in uni. I hope it can help you too.
- Input need first number is the number of rows. After that is the matrix with space between
- Every function is returning a new copy matrix or a value.
- The function is using 0-indexed (use with caution)
Input:
2
1 2
3 4
2
0 3
4 5
2
2 x
5x^2 10
Samples
# Get the matrix from stdin
# You can do t=Fraction for precision (Poly is not compatible with Fraction yet)
# t = float, t=int
a = Matrix()
b = Matrix()
c = Matrix(t=Poly) # Need to use for poly class to use variables
# Specify the type
a = Matrix(t=Fraction)
a = Matrix(t=int)
a = Matrix(t=float)
a = Matrix(t=complex)
# Intialize from 2D arrays
arr = [[1,2], [3,4]]
a = Matrix(a=arr)
# Show the array
# Expected output:
# 1 2
# 3 4
# [[1,2],[3,4]]
a.show() # Show the matrix with spacing and no brackets
a.print_l() # Show as a 2D array
# Operations (Return a new matrix)
a * b # Multiply 2 matrices
a * 2 # Apply to all elements (Haven't support the left multiply -> You can't do 2 * a)
a + b # Add 2 matrices
a - b # Subtract 2 matrices
a**10 # Matrix exponential (Use binary exponential) -> FAST
a == b # Check if 2 matrices are identical
# Get copies
a._copyArr() # Get the copy of 2D list of matrix
a._copyMat() # Get the new copy of current matrix
# Assigning rows
# b_delta, b_row, a_delta, a_row, applied row
# used for RREF and other algorithms
a.assignRow(2, 0, 1, 1, 1) # This means apply to -> row 1 = 2*(row 0) + 1*(row 1) (Zero indexed)
a.swapRow(0,1) # Swap row 0 and 1
a.swapCol(0,1) # Swap column 0 and 1 (In future update)
a.removeRow(0) # Remove row 0
a.removeCol(1) # Remove column 1
# Special operations
a.T() # Get the transpose
a.inv() # Get the inverse of A if exist (Updated: You can switch between Matrix Inversion Algorithm or inverse by Determinant And Adjungate)
a.rot90() # Rotate clockwise 90 degrees
a.concat(b) # Connect 2 matrices to create augmented matrix (Concat sideway) (in_place=False by default)
a.rref() # Get the Reduced Row Echelon Form of the matrix
# Static, global methods
Matrix.isinv(a, b) # Check if 2 matrices are inverses
Matrix.im(10) # Create an identical matrix with type array of size n
Matrix.imat(10) # Return an identical matrix with type Matrix
Matrix.mvector([1,2,3]) # Create a vertical vector (very convenient for linear transformation and spectral)
Matrix.zero_vec() # Get the zero vector
# Checking
a.isrref() # check if this matrix is in Reduced Row Echelon Form
a.isrref(arr=[[0,1],[0,0]]) # check another array
# Determinant, minor, cofactor
a.minor(1, 3) # Minor of the matrix if remove row 2 and column 4
a.cof(1,3) # Get the cofactor of this minor matrix by multiply with corresponding sign
a.sign_cof(1,3) # You can get the sign using this function
a.cofMat() # Give you a whole new matrix, which entry (i,j) is cofactor of the minor matrix (i,j)
a.adj() # Give you the adjungate matrix
a.det2d() # Find determinant of 2d matrix (Must strictly 2d)
a.det3d() # Find determinant of 3d matrix (Use Sarrus rule)
a.det() # A more general use. Find determinant of matrix (any size) (Can switch between using Cofactor Method or Adjungate Method)
a.solve(Matrix(a=[[1],[2],[3]])) # Use Cramers' Rule to solve
# Linear transformation
a.cA() # Characteristic Polynomial
a.vR(0) # For vertical vector, get the value at the "pos" row
a.is_vector() # Help to check if it is vertical vector
a.cB([Matrix(), Matrix(), Matrix()]) # Get coordinate vector according to a list of basis
a.eigen_values() # Get all eigen values of this matrix
# EXAMPLE SETUP
def func(vec: Matrix):
row1 = [vec.vR(0)+2*vec.vR(1)]
row2 = [vec.vR(0) - vec.vR(1)]
return Matrix(a=[row1, row2])
lt = LinearTransformation(2, 2, func)
B = [Matrix(), Matrix()]
D = [Matrix(), Matrix()]
# END
# Static methods
LinearTransformation.get_standard_basis() # A generator for you to get standard basis in Rn (Ex: for basis in LinearTransformation.get_standard_basis())
lt.get_transform_mat() # Get matrix A (the transform matrix of the linear transformation)
lt.transform(Matrix(a=[[1],[2]]) # Transform a vector
lt.get_transform_ADB(B,D) # Get the transform matrix A (from Rn to Rm where B is the basis in Rn and D is the basis in Rm)
lt.get_inverse_transform_func() # You can get the inverse function of the linear transformation from this
lt.inv_transform(Matrix(a=[[1],[2]])) # This one is simimlar to transform but using inverse function
# Spectral theory
a.is_similar(Matrix(a=[[1],[2],[3]])) # In progress, not guarantee similar now
a.eigen_vec(5) # Give you the rref solution of the eigen vector from corresponding eigen value
a.algebraic_multiplicity(5) # Give you the algebraic multiplicity of the eigen value
a.geometric_multiplicity(5) # Give you the geometric multiplicity of the eigen value
a.is_diagnolizable() # Can this matrix be diagonalized
a.diag() # Get the matrix D (the diagonal matrix) # Declare a function
def f1(x1,x2,x3):
return x1 and not(x2 or x3)
def f2(x1,x2,x3):
return x1 or (x2 and not x3)
# Check if 2 functions have same boolean for all cases
checkEqual(f1, f2, 3) # 3 is the number of variables used in f1 and f2
# Generate truth tables for function
generateTable(f1, 3) # 3 is the number of variables used in f1
generateTable(f1, 3, labels=["a", "b", "c"]) # Set the labels at the top of row
# More examples of custom function
# Can return multiple outputs 0 or 1
def half_adder(x1, x2):
summ = x1 ^ x2
carry = x1 and x2
return summ, carry