# Defining scalars (as floats, not ints)
a = 5.0
b = 4.0
# Addition, Subtraction, Multiplication, Division
add = a+b
sub = a-b
mul = a*b
div = a/b
print("Scalar Math:", add, sub, mul, div)
# Multiplication with Parentheses
# Multiplication is not implicit.
mul_paren = (a+b)*(a-b)
print("Multiplication with Partentheses:", mul_paren)Scalar Math: 9 1 20 1.25
Multiplication with Partentheses: 9import numpy as np
# Define a complex number
z = 4+3j
print("Complex Number:", z)
# Find the complex conjugate
z_conj = z.conjugate()
print("Complex Conjugate:", z_conj)
# Find the modulus and modulus squared
# Note that the modulus and modulus squared are still
# complex numbers
z_mod_squared = z*z_conj
z_mod = np.sqrt(z_mod_squared)
print("Modulus Squared and Modulus:", z_mod_squared, z_mod)
# Basic Arithmetic
x = 1+2j
y = 3-4j
print("Complex Number Math:", x+y, x-y, x*y)Complex Number: (4+3j)
Complex Conjugate: (4-3j)
Modulus Squared and Modulus: (25+0j) (5+0j)
Complex Number Math: (4-2j) (-2+6j) (11+2j)import numpy as np
# Define vectors as Numpy arrays
a = np.array([1,2,3])
b = np.array([4,5,6])
c = 10
# Arithmetic with Vectors
add = a+b
sub = a-b
mul = c*a
print("Vector Math:", add, sub, mul)
# Dot product two ways
dot1 = np.dot(a,b) #Order is important
dot2 = a.dot(b) # Order is important
print("Dot Product:", dot1, dot2)
# Cross product
cross = np.cross(a,b)
print("Cross Product:", cross)
# Magnitude and unit vector
mag = np.linalg.norm(a)
unit_vector = a/mag
unit_vector_mag = np.linalg.norm(unit_vector)
print("Magnitude, Unit Vector, Magnitude of Unit Vector:", mag, unit_vector, unit_vector_mag)Vector Math: [5 7 9] [-3 -3 -3] [10 20 30]
Dot Product: 32 32
Cross Product: [-3 6 -3]
Magnitude, Unit Vector, Magnitude of Unit Vector: 3.7416573867739413 [0.26726124 0.53452248 0.80178373] 1.0import numpy as np
# Matrices are defined as two-dimensional Numpy arrays
A = np.array([[1,2,3], [4,5,6], [7,8,9]])
B = np.array([[9,8,7], [6,5,4], [3,2,1]])
# Define a vector
x = np.array([2,4,6])
# Define a scalar
c = 10
# Matrix addition and subtraction
add = A+B
sub = A-B
print("Matrix Addition:", add)
print("Matrix Subtraction:", sub)
print()
# Matrix-matrix multiplication
# Do not use the * symbol!!
mul1 = A@B
mul2 = B@A
commutator = mul1 - mul2
print("Matrix Multiplication 1:",mul1)
print("Matrix Multiplication 2:", mul2)
print("Commutator:", commutator)
print()
# Matrix-Vector Multiplication
mul3 = A@x
print("Matrix-Vector Multiplication:", mul3)
print()
# Matrix-Scalar Multiplication
# Use the * symbol!!
mul4 = c*B
print("Matrix-Scalar Multiplixation:", mul4)
print()
# Transpose and Adjoint
transpose = A.T
adjoint = np.conj(B).T
print("Transpose:", transpose)
print("Adjoint:", adjoint)
print()
# Eigenvalues and Eigenvectors
# Note that the eigenvectors of A are the columns of the matrix
# eigenvectors
eigenvalues, eigenvectors = np.linalg.eig(A)
print("Eigenvalues:",eigenvalues)
print("Eigenvectors:",eigenvectors)Matrix Addition: [[10 10 10]
[10 10 10]
[10 10 10]]
Matrix Subtraction: [[-8 -6 -4]
[-2 0 2]
[ 4 6 8]]
Matrix Multiplication 1: [[ 30 24 18]
[ 84 69 54]
[138 114 90]]
Matrix Multiplication 2: [[ 90 114 138]
[ 54 69 84]
[ 18 24 30]]
Commutator: [[ -60 -90 -120]
[ 30 0 -30]
[ 120 90 60]]
Matrix-Vector Multiplication: [ 28 64 100]
Matrix-Scalar Multiplixation: [[90 80 70]
[60 50 40]
[30 20 10]]
Transpose: [[1 4 7]
[2 5 8]
[3 6 9]]
Adjoint: [[9 6 3]
[8 5 2]
[7 4 1]]
Eigenvalues: [ 1.61168440e+01 -1.11684397e+00 -8.58274334e-16]
Eigenvectors: [[-0.23197069 -0.78583024 0.40824829]
[-0.52532209 -0.08675134 -0.81649658]
[-0.8186735 0.61232756 0.40824829]]