Linear Algebra: Foundations and Applications

Master the core principles of linear algebra and its practical applications in data science, machine learning, and beyond.
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Fundamentals of Vectors and Vector Spaces

Unit 1: Introduction to Vectors

Unit 2: Exploring Vector Spaces

Unit 3: Linear Independence and Basis

Matrix Operations, Properties, and Linear Systems

Unit 1: Matrix Arithmetic

Unit 2: Determinants and Inverses

Unit 3: Rank, Nullity and Trace

Unit 4: Solving Linear Systems

Eigenvalues, Eigenvectors, and Diagonalization

Unit 1: Introduction to Eigenvalues and Eigenvectors

Unit 2: Properties and Applications of Eigenvalues and Eigenvectors

Unit 3: Diagonalization

Linear Transformations and Inner Product Spaces

Unit 1: Introduction to Linear Transformations

Unit 2: Kernel, Range, and Isomorphisms

Unit 3: Inner Product Spaces and Orthogonality

Applications in Data Analysis and Machine Learning

Unit 1: Singular Value Decomposition (SVD) for Dimensionality Reduction

Unit 2: Principal Component Analysis (PCA)

Unit 3: Linear Regression and Recommendation Systems

Emerging Trends and Software Applications

Unit 1: Linear Algebra in Quantum Computing

Unit 2: Software Applications: NumPy

Unit 3: Software Applications: MATLAB

Unit 4: Software Applications: R

Unit 5: Real-World Applications