Orthogonality and Orthogonal Bases

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Covers the theorems related to orthogonal projection and orthonormal bases.

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

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

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

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

Explains linear independence, basis, and matrix rank with examples and exercises.

Explores the concept of orthogonal complement in vector subspaces and fundamental matrix subspaces.

Explores vector spaces in three dimensions, covering linear combinations, subspaces, and properties of families of vectors in R³.

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

Explores the fundamentals of Singular Value Decomposition, including orthonormal bases and practical applications.