Linear Algebra Basics: Vector Spaces, Transformations, Eigenvalues

Related lectures (23)

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Explores normal equations, pseudo-solutions, unique solutions, and symmetric matrices in linear algebra.

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

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

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

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

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

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

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

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

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