Sylvester's Theorem: Orthogonal Bases

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

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

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

Covers the Gram-Schmidt algorithm for orthonormal bases in vector spaces.

Covers linear independence, bases, and coordinate systems with examples and theorems.

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

Covers orthogonal bases and Hermitian forms in linear algebra.

Explores the properties and applications of orthogonal matrices in linear algebra, focusing on orthogonality and projections.

Emphasizes the importance of using orthogonal bases in linear algebra for representing linear transformations.

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