Scalar Product and Euclidean Spaces

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Introduces the basics of real vector spaces, norms, and scalar products.

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Explores the definition and properties of Hermitian forms in complex vector spaces.

Explores the algebraic properties of the scalar product and their geometric implications.

Explores quadratic forms, symmetric bilinear forms, and their properties.

Covers the definition and properties of the scalar product, including geometric interpretations and algebraic properties.

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

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

Explores the properties of orthonormal vectors in Euclidean space through key equations and demonstrations.