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Scalar Multiplication Property 2 | Linear Algebra using Python

Linear Algebra using Python | Scalar Multiplication Property 2: Here, we are going to learn about the scalar multiplication property 2 and its implementation in Python.
Submitted by Anuj Singh, on May 26, 2020

Prerequisites:

• Defining a Vectors

Linear algebra is the branch of mathematics concerning linear equations by using vector spaces and through matrices. In other words, a vector is a matrix in n-dimensional space with only one column. In a scalar product, each component of the vector is multiplied by the same scalar value. As a result, the vector’s length is increased by a scalar value.

For example: Let a vector a = [4, 9, 7], this is a 3 dimensional vector (x,y and z)

So, a scalar product will be given as b = c*a

Where c is a constant scalar value (from the set of all real numbers R). The length vector b is c times the length of vector a. This scalar, multiplication follows a property shown below:

    cA + dA = (c + d)A

Where A and B are two vectors. The python code aims to evaluate the right-hand side and left-hand side for proving the scalar property.

Python code for scalar multiplication property 2

# Vectors in Linear Algebra Sequnce 
# Scalar Multiplication Property 2

A = [3, 5, -5, 8]
B = [7 , 7 , 7 , 7]

print("Vector A = ", A)
print("Vector B = ", B)

C = int(input("Enter the value of scalar multiplier c: "))
D = int(input("Enter the value of scalar multiplier d: "))

# Defining a function for scalar multiplication
def scalar(C, a):
    b = []
    for i in range(len(a)):
        b.append(C*a[i])
    return b    

# Defining a function for addition
def add(a,b):
    c = []
    for i in range(len(a)):
        c.append(a[i]+b[i])
    return c


# RHS
print("Vector (c + d)A = ", scalar(C+D,A))
    
# LHS    
An = scalar(C, A)
Bn = scalar(D, A)
print("Vector (cA + dA) = ", add(An,Bn))

print('---Both are same and therefore, the scalar property in vectors satisfies this property---')

Output:

Vector A =  [3, 5, -5, 8]
Vector B =  [7, 7, 7, 7]
Enter the value of scalar multiplier c: 5
Enter the value of scalar multiplier d: 2
Vector (c + d)A =  [21, 35, -35, 56]
Vector (cA + dA) =  [21, 35, -35, 56]
---Both are same and therefore, the scalar property in vectors satisfies this property---