Orthogonal Projections in Linear Algebra

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This lecture covers the concept of orthogonal projections in linear algebra, focusing on the properties of orthogonal matrices, projection onto subspaces, and the Gram-Schmidt process for orthonormal bases. The instructor explains the justification and application of theorems related to orthogonal projections, including the construction of orthogonal bases, the QR factorization of matrices, and the importance of orthogonal bases in regression analysis.

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Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Related lectures (24)

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Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Related lectures (24)

Orthogonality and Projection

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

Orthogonal Bases and Projection

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

Orthogonal Projection Theorems

Covers the theorems related to orthogonal projection and orthonormal bases.

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.

Orthogonal Families and Projections

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