Matrices and Orthogonal Transformations

Related lectures (31)

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

Explores the equivalence conditions for orthogonal matrices and includes examples of rotations.

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

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

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

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

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

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

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

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