#linear algebra

• Algebra — A foundational branch of mathematics that studies arithmetic operations and structural relations by generalizing the properties of numbers using symbols, letters, and variables. Broadly, it designates the study of abstract structures and polynomial equations.
• Annihilator — Producing annihilation; a device, force, agent, or structural element that has the capacity to completely destroy, reduce to zero, or fully neutralize another entity or phenomenon with which it comes into contact or upon which it acts directly. In mathematics and linear algebra, it describes a structure (an ideal or a set of operators) that completely nullifies the elements of a given space or structural module.
• Antisymmetric — Possessing the property of antisymmetry; changing its algebraic sign upon the inversion of elements (in mathematics and physics) or involving a binary relation where if one element relates to a second and vice versa, then the two elements are necessarily identical (in logic and set theory). In linear algebra, the term describes square matrices whose transpose equals their negative.
• Antisymmetry — A structural property of certain binary relations, functions, matrices, or physical systems of being antisymmetric. In logic and set theory, it represents the quality of a relation whereby if an element x relates to y and y relates to x, it necessarily follows that x equals y; in algebra and quantum physics, it defines the inversion of the sign of a function or tensor upon the interchanging of components or particles.