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Concept

Orthogonal basis

Related lectures (29)

Explores different types of basis sets, polarization functions, and accuracy challenges in computational chemistry.

Explores the vibration of diatomic AB molecules and Fourier series, emphasizing equations of motion and Dirichlet's theorem.

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Covers the analytical study of the plan, focusing on points and lines.

Discusses isometries and orthonormal bases in mathematics.

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Explores the fundamental theorem on singular values and the formation of orthonormal bases from eigenvectors.

Covers the analytical study of space, focusing on points, lines, and planes.

Explores polynomial approximation with orthonormal bases and orthogonal projection methods.

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

Covers the concept of an orthogonal basis in a vector space.

Covers finding the best quadratic approximation for a given function in a continuous space.

Explores the equivalence conditions for orthogonal matrices and includes examples of rotations.

Covers the decomposition of Eisenstein series into orthogonal components and the unitarizability of certain representations.

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Covers the theorems related to orthogonal projection and orthonormal bases.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

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

Introduces the Gram-Schmidt orthogonalization process to find orthogonal bases for vector subspaces.

Explores the spectral theorem, Coxeter graphs, eigenvalues, and determinants of positive definite matrices.