Linear Algebra Basics: Matrix Representations and Transformations

Related lectures (23)

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Explains orthogonal projection in linear algebra, focusing on transforming non-orthogonal bases into orthogonal ones.

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Explores matrix operations, rank determination, kernel dimensions, and basis concepts in linear algebra.

Explores injective and surjective linear transformations, kernel, image, and matrix operations.

Explores matrices, inverses, and their applications in linear algebra, emphasizing composition and transformation properties.

Explores the Eigen library for linear algebra, covering vectors, matrices, arrays, memory management, reshaping, and per-component operations.

Explores projections in R³, matrix properties, and trace concepts with practical examples.

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Explores geometric transformations in R2 and R3, including linear transformations, projections, matrices, and trace properties.

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.