Scalar Product and Euclidean Spaces

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Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

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

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Covers the definition and properties of vector spaces, along with examples like Euclidean spaces and matrix spaces.

Explores norm, dot product, and orthogonality in vector spaces, including properties and inequalities.

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

Covers the definition of a scalar product on a real vector space and provides examples.

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

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

Covers the main points of special relativity, including symmetries, transformations, 4-vectors, Maxwell equations, and proper time.