Lectures related to Vector Calculus: Direct Frame

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Introduces vector components, scalar and vector products, and their properties, including colinear and coplanar vectors, and the rule of the right hand.

Matrix Similarity and Diagonalization

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.

Linear Algebra: Vector Spaces

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.