Linear Algebra: Dot Product and Pre-Hilbertian Spaces

Related lectures (29)

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

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

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

Explores orthogonality, dot product properties, vector norms, and angle definitions in vector spaces.

Covers the definition of norm, distance between vectors, and Cauchy-Schwarz inequality.

Explores the properties and applications of the dot product in vector spaces.

Covers the representation of signals in vector spaces and inner product spaces, including the Projection Theorem.

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

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

Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.