Vector Equations and Linear Combinations

Related lectures (24)

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Introduces linear combinations of vectors in R^n and their properties.

Covers linear independence, bases, and coordinate systems with examples and theorems.

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Covers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.

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

Explores vector spaces, linear independence, and spanning sets in linear algebra.

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

Covers vector spaces, subspaces, kernel, image, linear independence, and bases in linear algebra.

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

Explores linear dependence and independence of vectors, including subspaces generation and corollaries.