Orthogonality and Scalar Product

Related lectures (30)

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

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

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Introduces function spaces and Hilbert spaces, discussing inner product spaces and the importance of completeness in Hilbert spaces.

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

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

Covers the definition of scalar product, properties, examples, and applications in Euclidean spaces, including the Cauchy-Schwartz inequality.

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

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