Scalar Product and Euclidean Spaces

In course

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Description

This lecture covers the definition of a scalar product and its properties in Euclidean spaces, including bilinearity, symmetry, and positive definiteness. Examples and applications of the standard scalar product in real spaces are also discussed, along with the Cauchy-Schwartz inequality. The lecture further explores quadratic forms, norm verification, and geometric interpretations of scalar products in finite-dimensional real vector spaces.

Instructor

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Official source

https://mediaspace.epfl.ch/media/0_gy1oo6cv

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Ontological neighbourhood

Mathematics

Algebra: Linear algebra

Analysis: Functional analysis, Tensor analysis

Geometry: Euclidean geometry

Mechanical engineering

Aerospace engineering: Spacecrafts

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