Linear Algebra

Study of linear algebra transformations including matrix-based rotation, scaling, and centering of data, along with combining transformations, computing centroids, and solving linear systems using matrix inverses. Covers 2×2 matrix inverses, Gaussian elimination, and applications in solving Ax = B.

Lecture 92 June 2026

Vector Spaces, Row Space, and Column Space in Linear Algebra

Understanding vector spaces in linear algebra including axioms of vector spaces, linear combinations, span, basis, row space, and column space of matrices. Covers key concepts of linear independence, Gaussian elimination, and how matrix transformations relate to solving systems of linear equations.

Lecture 9 109 June 2026

Vector Spaces, Row Spaces, Column Spaces, and Null Spaces

A complete guide to fundamental linear algebra spaces. Covers the 8 vector space axioms, subspace rules, linear combinations, span, basis, dimension, finding bases for row, column, and null spaces via RREF, and applying the Rank-Nullity Theorem.

Lecture 1115 June 2026

Linear Independence, Unit Vectors, Orthogonality, Norms, Determinants, Eigenvalues and Eigenvectors in Linear Algebra

Understanding advanced linear algebra concepts including linear independence and dependence, unit vectors, vector normalization, orthogonal and orthonormal bases, vector and matrix norms, determinants, eigenvalues, eigenvectors, and eigen decomposition. Covers important concepts used in matrix transformations, data representation, dimensionality reduction, and machine learning applications.

Lecture 1223 June 2026

Eigenvalues, Eigenvectors, Characteristic Equation, and Eigen Decomposition in Linear Algebra

Understanding eigenvalues and eigenvectors, their relationship with matrix transformations, characteristic equations, finding eigenvalues and eigenvectors, special cases of matrices, and their applications in data compression, machine learning, and dimensionality reduction. Covers vector norms, Frobenius norm, determinants, and how these concepts are used in eigen decomposition.

Lecture 12-1330 June 2026

Vector Norms, Determinants, Eigenvalues, Eigenvectors, and Eigen Decomposition in Linear Algebra

A comprehensive study of vector and matrix norms, including L1, L2, and Frobenius norms, determinants of matrices, characteristic polynomials, eigenvalues, eigenvectors, and eigen decomposition. Covers methods for computing eigenvalues and eigenvectors, interpreting linear transformations, and understanding their applications in data analysis, machine learning, computer graphics, and matrix factorization.

Lecture 14-157 July 2026

Linear Algebra Study Guide: Eigenvalue Decomposition & Singular Value Decomposition

A comprehensive, textbook-quality study guide covering matrix inverses, diagonal properties, Eigenvalue Decomposition (EVD), and Singular Value Decomposition (SVD) with step-by-step mathematical proofs and examples.