Quadratic Forms and Symmetries

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Covers the joint equidistribution of CM points in algebraic structures and quadratic forms.

Explores symmetric matrices, diagonalization, and quadratic forms properties.

Explores symmetric matrices, quadratic forms, diagonalization, and definiteness with examples and calculations.

Explores quadratic forms, symmetric bilinear forms, and their properties.

Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.

Delves into Oppenheim's conjecture on quadratic forms and their connection to number theory.

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Covers the proof of the recursive formula for the optimal gains in LQ control over a finite horizon.

Explores the classification of quadratic forms based on eigenvalues and orthogonal diagonalization of symmetric matrices.

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