Linear Transformations and Change of Bases

Related lectures (25)

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Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Covers linear applications, matrices, transformations, and the principle of superposition.

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

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

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Explores the relationship between matrices under different bases in linear algebra.

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

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Covers the reduction of a linear application and finding corresponding reduced forms and bases.