MATH-111(f): Linear Algebra

Lectures in this course (62)

Explores linear maps, matrix properties, and operations on matrices.

Explores injectivity and surjectivity in linear maps through examples and proofs.

Explores matrix arithmetic, including properties, products, and dimensions, with a focus on matrix multiplication and commutativity.

Explores matrix multiplication, its properties, and applications in linear maps.

Explores the matrix associated with reciprocal maps and properties of invertible matrices.

Explores the properties and applications of matrix transpose, including rotations and inverse matrices.

Explores properties of invertible matrices and demonstrates the Gauss algorithm for matrix inversion.

Explores the definitions and properties of invertible matrices, including determinants and uniqueness of solutions.

Explains the common properties of determinants and their consequences.

Explores the fundamental properties of determinants, including left vs. right multiplication and the Sarrus rule for 3x3 matrices.

Explores determinants, areas, and volumes in matrices, emphasizing their geometric interpretations and applications in linear transformations.

Explores alternative definitions of determinants, properties of matrices, geometric interpretations, and the Gauss algorithm.

Covers the definition and properties of vector spaces, along with examples like Euclidean spaces and matrix spaces.

Explores area determination, linear applications, matrix operations, and vector spaces.

Explores linear applications in vector spaces, emphasizing subspaces and properties of linear maps.

Explores the construction and properties of vector subspaces through examples and fundamental concepts.

Explores forming bases, dependencies, and relationships in linear applications using invertible matrices and canonical bases.

Explores properties of linear applications, including symmetric matrices and linearity in analysis.

Explores linear combinations, basis determination, and vector space dimensionality through practical examples and exercises.

Covers components and bases in vector spaces, demonstrating linearity and injectivity.

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