Orthogonal Projections and Best Approximation

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Explains orthogonal projection and vector decomposition with examples in particle trajectory analysis.

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

Explores orthogonality, norms, and distances in vector spaces for solving linear systems.

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

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

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

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

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

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

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.