Mathematical Operations

Basic Mathematical Operations

Let's start with a simple NumPy array:

import numpy as np

numbers = np.array([10, 20, 30, 40])

print(numbers)

NumPy allows you to perform calculations directly on the entire array.

print(numbers + 5)
print(numbers - 5)
print(numbers * 5)
print(numbers / 5)

[15 25 35 45]
[ 5 15 25 35]
[ 50 100 150 200]
[2. 4. 6. 8.]

NumPy automatically applies the operation to every element.

Addition

You can add a number to every element in an array.

prices = np.array([100, 200, 300])

result = prices + 50

print(result)

[150 250 350]

NumPy performs:

100 + 50 = 150
200 + 50 = 250
300 + 50 = 350

You do not need a for loop for this.

Subtraction

Subtraction works in the same way.

prices = np.array([100, 200, 300])

result = prices - 20

print(result)

[ 80 180 280]

The value 20 is subtracted from every element.

Multiplication

Multiplication can also be performed on the entire array.

numbers = np.array([2, 4, 6, 8])

result = numbers * 3

print(result)

[ 6 12 18 24]

Each value is multiplied by 3.

Division

Division works the same way.

numbers = np.array([10, 20, 30, 40])

result = numbers / 10

print(result)

[1. 2. 3. 4.]

Notice that NumPy returns floating-point values such as 1.0, 2.0, and so on.

Operations Between Two Arrays

Mathematical operations can also be performed between two arrays of compatible shapes.

a = np.array([10, 20, 30])

b = np.array([1, 2, 3])

result = a + b

print(result)

[11 22 33]

NumPy performs the operation element by element:

10 + 1 = 11
20 + 2 = 22
30 + 3 = 33

Multiplying Two Arrays

prices = np.array([100, 200, 300])

quantity = np.array([2, 3, 4])

total = prices * quantity

print(total)

[ 200  600 1200]

Each price is multiplied by its corresponding quantity.

100 × 2 = 200
200 × 3 = 600
300 × 4 = 1200

This type of element-by-element calculation is very common when working with numerical data.

Sum of an Array

The sum() function adds all values in an array.

numbers = np.array([10, 20, 30, 40])

total = np.sum(numbers)

print(total)

100

NumPy calculates:

10 + 20 + 30 + 40 = 100

Mean

The mean is the average of the values.

scores = np.array([70, 80, 90, 100])

average = np.mean(scores)

print(average)

85.0

The calculation is:

(70 + 80 + 90 + 100) / 4 = 85

Mean is especially useful when analyzing datasets and model metrics.

Minimum and Maximum

You can find the smallest value using np.min().

numbers = np.array([15, 8, 42, 23, 10])

print(np.min(numbers))

8

The largest value can be found using np.max().

print(np.max(numbers))

42

Standard Deviation

Standard deviation tells us how spread out values are from the average.

scores = np.array([70, 75, 80, 85, 90])

std = np.std(scores)

print(std)

7.0710678118654755

A smaller standard deviation generally means the values are closer together, while a larger value means they are more spread out.

This becomes useful in statistics and Machine Learning when understanding the distribution of data.

Absolute Value

The absolute value removes the negative sign from a number.

numbers = np.array([-10, -5, 0, 5, 10])

result = np.abs(numbers)

print(result)

[10  5  0  5 10]

For example:

-10 → 10
-5  → 5
 0  → 0
 5  → 5
10  → 10

Power

The np.power() function raises values to a specified power.

numbers = np.array([2, 3, 4])

result = np.power(numbers, 2)

print(result)

[ 4  9 16]

This means:

2² = 4
3² = 9
4² = 16

Square Root

NumPy provides np.sqrt() for calculating square roots.

numbers = np.array([4, 9, 16, 25])

result = np.sqrt(numbers)

print(result)

[2. 3. 4. 5.]

Rounding Numbers

You can round decimal values using np.round().

numbers = np.array([
    1.234,
    5.678,
    9.876
])

result = np.round(numbers, 2)

print(result)

[1.23 5.68 9.88]

The second argument, 2, means that we want two decimal places.

Mathematical Functions

NumPy also provides many mathematical functions such as sine, cosine, logarithms, and exponentials.

For example, you can calculate the exponential of values:

numbers = np.array([1, 2, 3])

result = np.exp(numbers)

print(result)

NumPy can therefore handle much more than simple addition and subtraction.

Mathematical Operations on 2D Arrays

Mathematical operations become especially useful when working with two-dimensional datasets.

data = np.array([
    [10, 20, 30],
    [40, 50, 60]
])

print(np.sum(data))

210

NumPy adds every value in the entire array.

You can also calculate values row by row using axis=1.

print(np.sum(data, axis=1))

[ 60 150]

The first row is 10 + 20 + 30 = 60, and the second row is 40 + 50 + 60 = 150.

Operations by Column

With axis=0, NumPy performs the operation down the rows, which gives a result for each column.

data = np.array([
    [10, 20, 30],
    [40, 50, 60]
])

print(np.sum(data, axis=0))

[50 70 90]

NumPy calculates:

10 + 40 = 50
20 + 50 = 70
30 + 60 = 90

Mathematical Operations in AI

Mathematical operations are everywhere in AI and Machine Learning.

For example, imagine model prediction errors:

errors = np.array([
    2.5,
    -1.5,
    3.0,
    -2.0,
    1.0
])

We can calculate the average error:

average_error = np.mean(errors)

print(average_error)

0.6

We can also remove negative signs when we only care about the size of the error:

absolute_errors = np.abs(errors)

print(absolute_errors)

[2.5 1.5 3.  2.  1. ]

This kind of numerical processing is fundamental when evaluating and preparing data for AI models.

Example: Finding the Average and Scaling Data

Suppose we have some values:

data = np.array([10, 20, 30, 40, 50])

mean = np.mean(data)

print(mean)

30.0

We can then subtract the mean from every value:

centered = data - mean

print(centered)

[-20. -10.   0.  10.  20.]

This is a simple example of transforming data around its mean. Similar mathematical transformations are commonly used when preparing data for Machine Learning.

NumPy Mathematical Functions

Complete Example

Here is a small example that combines several NumPy mathematical operations:

import numpy as np

scores = np.array([70, 80, 90, 100])

total = np.sum(scores)
average = np.mean(scores)
minimum = np.min(scores)
maximum = np.max(scores)

print("Total:", total)
print("Average:", average)
print("Minimum:", minimum)
print("Maximum:", maximum)

Total: 340
Average: 85.0
Minimum: 70
Maximum: 100

This is much simpler than manually calculating each value with Python loops.