Algebraic Structures and Crystallography

Related lectures (29)

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Covers the standard properties of distance and norm in vector spaces.

Explores the geometry of the plane and complex numbers in R².

Covers mathematical concepts related to vector operations and geometry, including scalar product and vector norms.

Introduces orthogonal and orthonormal families in vector spaces with scalar products.

Explores orthogonality, scalar product, and orthonormal bases in vector spaces.

Explores reciprocal lattice in 2D systems, diffraction from lattice and atomic structures, emphasizing scattering and constructive interference.

Explores Hilbert spaces, orthonormal systems, and the Bessel inequality, emphasizing their properties and significance.

Introduces Euclidean elements, explores infinity uniqueness, parallel lines, and different geometries like Euclidean, hyperbolic, and spherical.

Explores orthogonality, Gram-Schmidt process, dot products, and solution minimization in systems.