Vector spaces: Hilbert space

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Orthogonal Complement and Projection

Covers the concept of orthogonal complement and projection in vector spaces.

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.

Curves in the Oriented Plane

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

Orthogonal Families and Projections

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

Orthogonal Families and Projections

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

Orthogonality and Subspace Relations

Explores orthogonality between vectors and subspaces, demonstrating practical implications in matrix operations.

Crash Course on Quantum Mechanics

Offers a crash course on quantum mechanics, covering vector spaces, superposition, observables, and self-adjoint operators.

Vector Spaces Equivalence

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

Orthogonal Projection: Spectral Decomposition

Covers orthogonal projection, spectral decomposition, Gram-Schmidt process, and matrix factorization.