Linear Algebra: Organization and Exercises

Related lectures (24)

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

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.

Introduces orthogonal matrices, the least squares method, and their practical applications in linear algebra.

Explains eigenvalues and eigenvectors in linear algebra with practical examples and properties of matrix transformations.

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

Covers eigenvalues, eigenvectors, and diagonalization of matrices.

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

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

Introduces the Gram-Schmidt algorithm, QR factorization, and the method of least squares.

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.