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

Explores orthogonality, triangle inequality, and the Pythagorean theorem in vector spaces.

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

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

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

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

Introduces the Pythagorean theorem, explaining its geometric significance and applications in calculating areas.

Covers norm, scalar product, and perpendicularity in R^n, including the theorem of Pythagoras and orthogonal complements.

Introduces orthogonal vectors, scalar product, Euclidean norm, Pythagorean theorem, and unit vectors.

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

Explores vector geometry basics, historical perspectives, and practical applications.

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

Explores elementary operations in geometry, including addition, subtraction, multiplication, and division of segments and angles.

Introduces the first step in finding an orthogonal/orthonormal base in a vector space.

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

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

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

Covers matrix operations, scalar product, orthogonality, and bases in vector spaces.

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