6 papers
Linear algebra and group theory
Teo Banica
This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the…
Methods of free probability
Teo Banica
This is a joint introduction to classical and free probability, which are twin sisters. We first review the foundations of classical probability, notably with the main limiting the…
Principles of operator algebras
Teo Banica
This is an introduction to the algebras that the linear operators can form, once a complex Hilbert space is given. Motivated by quantum mechanics, we…
Quantum permutation groups
Teo Banica
The permutation group has a quantum analogue , which is infinite at . We review the known facts regarding , and notably its easiness property, Weingarte…
Affine noncommutative geometry
Teo Banica
This is an introduction to noncommutative geometry, from an affine viewpoint, that is, by using coordinates. The spaces have no free analogues in the oper…
Invitation to Hadamard matrices
Teo Banica
An Hadamard matrix is a square matrix whose rows and pairwise orthogonal. More generally, we can talk about the complex Hadamard matrices, which are the square mat…