Introduction to Linear Algebra
A comprehensive introduction to linear algebra, covering its fundamental concepts, importance in various fields, and how it serves as a foundation for data science, machine learning, and more.
Vectors and Their Operations
A comprehensive guide to understanding vectors, their properties, and essential operations, including addition, scalar multiplication, dot product, and cross product.
Matrix Operations
A comprehensive guide to understanding matrices, their operations, and properties, including addition, multiplication, transpose, determinants, inverses, and solving systems of equations using matrices.
Solving Systems of Linear Equations
A comprehensive guide to methods for solving systems of linear equations, including substitution, elimination, Gaussian elimination, and matrix methods like LU decomposition.
Vector Spaces and Subspaces
An in-depth exploration of vector spaces and subspaces, including their definitions, properties, and importance in linear algebra.
Geometric Interpretation of Vector Spaces
Understanding the geometric interpretation of vector spaces, including visualizing vectors, linear combinations, and subspaces in 2D and 3D.
Null Space, Column Space, and Rank
An in-depth exploration of the null space, column space, and rank of a matrix, including their significance in solving linear systems and applications in data science.
Orthogonality and Orthonormal Bases
An in-depth exploration of orthogonality, orthonormal bases, and their significance in simplifying linear transformations and data science applications like PCA.
Change of Basis and Its Applications
Understanding the concept of changing the basis in vector spaces and its applications in data science, including dimensionality reduction and data transformation.
Eigenvalues and Eigenvectors
A comprehensive guide to understanding eigenvalues and eigenvectors, their significance in linear algebra, and their applications in data science and beyond.