Matrices and Change of Bases

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

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

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Explores the application of linear algebra in quantum mechanics, emphasizing vector spaces, Hilbert spaces, and the spectral theorem.

Explores basis transformation, eigenvalues, and linear operators in inner product spaces, emphasizing their significance in Quantum Mechanics.

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

Covers the organization of linear algebra course and exercises for civil engineering and environmental sciences students.

Introduces linear algebra concepts, focusing on solving systems of linear equations and their representations.

Explores matrix representation of linear applications, emphasizing eigenvalues and bases.