Orthogonal Projections and Reflections

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Related lectures (28)

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Diagonalization of Linear Transformations

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.

Linear Algebra: Orthogonal Projection and QR Factorization

Explores Gram-Schmidt process, orthogonal projection, QR factorization, and least squares solutions for linear systems.

Subspaces, Spectra, and Projections

Explores subspaces, spectra, and projections in linear algebra, including symmetric matrices and orthogonal projections.

Orthogonal Projection on Straight Line

Explores orthogonal projection on straight lines in analytic geometry, focusing on projection matrices and symmetrical properties.

Orthogonal Families and Projections

Explains orthogonal families, bases, and projections in vector spaces.

Orthogonal Bases and Projection

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

Orthogonal Projections: Rectors and Norms

Covers orthogonal projections, rectors, norms, and geometric observations in vector spaces.

Translations and Homotheties

Covers translations, homotheties, and their analytical expressions, emphasizing stability by composition.

Linear Regression: Absence or Presence of Covariates

Explores linear regression with and without covariates, covering models captured by independent distributions and tools like subspaces and orthogonal projections.

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.