Linear algebra is the branch of mathematics that deals with vector spaces and matrices. It is the mathematics of data, dealing with its creation, representation, transformation, and consumption using various concepts of vectors and matrices.

In the world of data science, data is not only represented in the form of vectors and matrices but is also researched and transformed using various concepts of linear algebra. This makes it essential to know the concepts of linear algebra to better understand the inner workings of various machine learning models and algorithms.

This lab is part of a set of five labs. These labs aim to teach linear algebra with a special emphasis on coding examples and good visualization practices. This is achieved using Python and its libraries like Numpy, Matlplotlib, etc.

In this lab, you will learn the following:

• Basics of vectors
• Representing vectors in Numpy
• Visualizing vectors using Matplotlib
• Magnitude of a vector
• Unit vector
• Vector addition
• Scalar multiplication of vectors
• Vector subtraction
• Dot product
• Cross product

In this lab, you will learn the following:

• Vector spaces
• Plotting a vector space
• Linear transformation on a vector space
• Special linear transformations
• Basis vectors
• Changing basis
• Linear independence

In this lab, you will learn the following:

• Basics of matrices
• Representing matrices in Numpy
• Addition and Subtraction of matrices
• Matrix multiplication
• Scalar matrix multiplication
• Slicing and indexing
• Numpy functions for matrices

In this lab, you will learn the following:

• Determinant of a matrix
• Inverse of a matrix
• Row echelon form
• Reduced row echelon form
• Gaussian elimination

In this lab, you will learn the following:

• Eigenvalues and eigenvectors
• Eigendecomposition
• Matrix diagonalization