Norm, Dot Product, Orthogonality

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

Explores quadratic forms, symmetric bilinear forms, and their properties.

Explores polynomial operations, properties, and subspaces in vector spaces.

Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.

Explores orthogonality, triangle inequality, and the Pythagorean theorem in vector spaces.

Introduces orthogonal sets and bases, discussing their properties and linear independence.

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

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Explores orthogonality, scalar product, and orthonormal bases in vector spaces.

Covers the concept of orthogonal complement in Rn and related propositions and theorems.