Pfaffian: A function associated with a skew-symmetric matrix, playing a role analogous to the determinant for antisymmetric matrices, important in random matrix theory and integrable hierarchies.

By identifying these conditions, the mathematicians discovered when a square matrix can be broken down into special types of matrices called symplectic and skew-Hamiltonian.

CBSE Class 12th Mathematics Syllabus 2025-26: See the article below for a detailed explanation of the CBSE Class 12th Mathematics Syllabus 2025–2026, as well as a link to download the PDF.

HOLO constructs quantum states based on Matrix Product States (MPS) and leverages mirror symmetry to optimize the loading of probability distributions.