Lectures related to Gram-Schmidt Process

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

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

Projection in Vector Spaces

Explores the generalization of projection in vector spaces and its unique properties, emphasizing its role in finding the closest vector in a subspace.

Orthogonal Bases in Vector Spaces

Covers the concept of orthogonal bases in vector spaces and Pythagorean theorem applications.

Orthogonalization of Vectors

Covers the Gram-Schmidt orthogonalization process and vector projections in a vector space.

Orthogonal Complement and Projection

Covers the concept of orthogonal complement and projection in vector spaces.

Orthogonality and Projection

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

Orthogonal Projection Theorems

Covers the theorems related to orthogonal projection and orthonormal bases.

Orthogonal Families and Projections

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

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Orthogonal Families and Projections

Introduces orthogonal families, orthonormal bases, and projections in linear algebra.

Orthogonal Projection: Example and Additional Remarks

Explains orthogonal projection onto a subspace and finding orthogonal bases using Gram-Schmidt procedure.

Orthogonal Bases in Vector Spaces

Explores orthogonal bases in vector spaces, explaining unique vector representations and spectral decomposition.

Orthogonal Projection Theorem

Explores orthogonal projection calculation and orthonormal bases uniqueness through matrix operations.

Orthogonal Projection: Spectral Decomposition

Covers orthogonal projection, spectral decomposition, Gram-Schmidt process, and matrix factorization.

Orthogonal Bases in Vector Spaces

Covers orthogonal bases, Gram-Schmidt method, linear independence, and orthonormal matrices in vector spaces.

Orthogonal Projection on Vector Subspace

Explains orthogonal projection on a vector subspace in Euclidean space.

Finding Orthogonal/Orthonormal Base: First Step

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

Matrix Operations and Orthogonality

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

Vector Calculus in 3D

Covers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.