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Related lectures (38)

Covers the definition of scalar product, properties, examples, and applications in Euclidean spaces, including the Cauchy-Schwartz inequality.

Isometries in Euclidean Spaces

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

Vectors: Fundamentals

Covers the basic concepts related to vectors, including their definition, operations, and properties, as well as applications through examples and the Varignon's theorem.

Matrices and Orthogonal Transformations MOOC: Linear Algebra (Part 3)

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

Special Relativity

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

Vector Spaces: Properties and Examples Log in to Mediaspace to watch this video

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

Orthogonality and Gram-Schmidt Process Log in to Mediaspace to watch this video

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

Shells I: Mechanics of Slender Structures Log in to Mediaspace to watch this video

Covers linear and membrane theories of pressure vessels, differential geometry of surfaces, and the reduction of dimensionality from 3D to 2D.

Vectors: Definitions and Operations Log in to Mediaspace to watch this video

Introduces vector definitions, displacement, addition, and applications in geometry.

Linear Algebra: Linear Dependence and Independence Log in to Mediaspace to watch this video

Explores linear dependence and independence of vectors in geometric spaces.

Decomposition of a Vector Log in to Mediaspace to watch this video

Covers the decomposition of a vector in a base and its applications in speed and distance calculations.

Orthonormal Vectors Properties Log in to Mediaspace to watch this video

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

Linear Combinations: Vectors and Matrices Log in to Mediaspace to watch this video

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

Analytical Geometry: Vectors and Operations Log in to Mediaspace to watch this video

Covers the fundamentals of analytical geometry, focusing on vectors and their operations.

Linear Independence in Vector Spaces Log in to Mediaspace to watch this video

Explores linear independence in vector spaces and the concept of bases.

Physics 1: Vectors and Dot Product Log in to Mediaspace to watch this video

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

Polynomials: Operations and Properties Log in to Mediaspace to watch this video

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

Orthogonal Linear Maps Log in to Mediaspace to watch this video

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Rectilinear Movement: Vectors and Scalars Log in to Mediaspace to watch this video

Explores rectilinear movement, vector algebra, scalar products, and vector decomposition in a three-dimensional space.

Linear Transformations: Matrices and Applications Log in to Mediaspace to watch this video

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

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