Basics of Vectors and Matrices | CodeSignal Learn

Lesson Introduction

Welcome to this exciting course path! This path focuses on teaching math concepts that are important for machine learning. Note that this path assumes that you have basic knowledge of the python programming language. You can use our Introduction Programming in Python course path to gain or solidify this knowledge. Welcome to our lesson on the basics of vectors and matrices! In this lesson, we'll explore what vectors and matrices are, why they're important in machine learning, and how to create and work with them in Python. By the end of this lesson, you'll understand how to define, display, and interpret vectors and matrices. Let's get started!

Concept: Vector

\begin{bmatrix} 1 & 2 & 3 \end{bmatrix}

Creating and Displaying a Row Vector in Python

Let's see how we can create a row vector in Python using np.array() from the NumPy library. NumPy provides advanced linear algebra features that will be useful in the upcoming units of our course. Python import numpy as np # Create a row vector vector = np.array([1, 2, 3]) # Display the vector print("Vector:", vector) # Output: Vector: [1 2 3] This shows a simple row vector with three numbers.

Creating and Displaying a Column Vector in Python

And this is how we represent the column vector using np.array() : Python import numpy as np # Create a column vector vector = np.array([[1], [2], [3]]) # Display the vector print("Vector:", vector) # Output: Vector: [[1] [2] [3]] Using np.array(), we specify a 2-dimensional structure for the column vector, but with one item in each row.

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Basics of Vectors and Matrices | CodeSignal Learn

Creating and Displaying a Matrix in Python

Next, let's create a matrix using np.array() : import numpy as np # Create a matrix matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) # Display the matrix print("Matrix:", matrix) # Output: Matrix: [[1 2 3] [4 5 6] [7 8 9]] This is a 3x3 matrix, represented with a 2-dimensional NumPy array.

Getting Dimensions in Python: Vectors

Understanding the dimensions of vectors and matrices is essential for many operations in machine learning. Let's see how to print the length of a vector: import numpy as np # Create a row vector row_vector = np.array([1, 2, 3]) print("Length of the row vector:", len(row_vector)) # Output: Length of the row vector: 3 # Create a column vector column_vector = np.array([[1], [2], [3]]) print("Length of the column vector:", column_vector.shape[0]) # Output: 3 For np.array(), the length of a row vector can be found using len(), and for a column vector, we use the .shape attribute to get the number of rows.

Getting Dimensions in Python: Matrices

Here's how to get the number of rows and columns in a matrix: import numpy as np # Create a matrix matrix = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) # Number of rows num_rows = matrix.shape[0] print("Number of rows:", num_rows) # Output: Number of rows: 3 # Number of columns num_columns = matrix.shape[1] print("Number of columns:", num_columns) # Output: Number of columns: 3 Using the .shape attribute of np.array(), we can easily access both the number of rows and columns in a matrix. Now you know how to create and display vectors and matrices and determine their dimensions using np.array() from the NumPy library. This will provide the linear algebra features that are crucial for the upcoming units of our course.

Python

import numpy as np

# Create a matrix
matrix = np.array([
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
])

# Display the matrix
print("Matrix:", matrix)  # Output: Matrix: [[1 2 3] [4 5 6] [7 8 9]]

Python

import numpy as np

# Create a row vector
row_vector = np.array([1, 2, 3])
print("Length of the row vector:", len(row_vector))  
# Output: Length of the row vector: 3

# Create a column vector
column_vector = np.array([
    [1],
    [2],
    [3]
])
print("Length of the column vector:", column_vector.shape[0])  # Output: 3

Python

import numpy as np

# Create a matrix
matrix = np.array([
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
])

# Number of rows
num_rows = matrix.shape[0]
print("Number of rows:", num_rows)  # Output: Number of rows: 3

# Number of columns
num_columns = matrix.shape[1]
print("Number of columns:", num_columns)  # Output: Number of columns: 3