Linear Applications: Change of Basis

Related lectures (26)

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Covers bijective linear maps, invertibility of matrices, isomorphisms, and the rank theorem.

Explores bases in vector spaces, including linear combinations, orthogonal bases, and basis transformations using rotation matrices.

Explores canonical forms of matrices, matrix products, and linear applications in vector spaces.

Introduces linear applications in 3 dimensions, defining them as functions that preserve vector addition and scalar multiplication.

Explores the canonical basis in linear algebra, focusing on matrix representation, diagonalizability, and characteristic polynomials.

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

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

Explores change of basis matrices in linear algebra, emphasizing the importance of understanding matrix transformations between different bases.

Covers tensor products, symmetric power, and exterior power of vector spaces, including properties and applications.

Covers vector spaces, bases, and decomposition of vectors in R³.