Algebraic Structures: Fields and Vectorial Spaces

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Covers algebraic structures, crystallography, crystal structures, and Euclidean geometry with a focus on vectors and crystal planes.

Explores polynomial operations, properties, and subspaces in vector spaces.

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

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

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Covers groups, rings, number theory, atomic bonds, and materials structure, setting the foundation for further exploration.

Covers the properties of vectors, including commutativity, distributivity, and linearity.

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.