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This glossary of linear algebra is a list of definitions and terms relevant to the field of linear algebra, the branch of mathematics concerned with linear equations and their representations as vector spaces. For a glossary related to the generalization of vector spaces through modules, see glossary of module theory
Concerning general linear maps, linear endomorphisms, and square matrices have some specific properties that make their study an important part of linear algebra, which is used in many parts of mathematics, including geometric transformations, coordinate changes, quadratic forms, and many other parts of mathematics.
Each such part is called a ray and the point A is called its initial point. It is also known as half-line (sometimes, a half-axis if it plays a distinct role, e.g., as part of a coordinate axis). It is a one-dimensional half-space. The point A is considered to be a member of the ray.
The open (closed) upper half-space is the half-space of all (x 1, x 2, ..., x n) such that x n > 0 (≥ 0). The open (closed) lower half-space is defined similarly, by requiring that x n be negative (non-positive). A half-space may be specified by a linear inequality, derived from the linear equation that specifies the defining hyperplane.
Mathematics and art are related in a variety of ways. For instance, the theory of perspective showed that there is more to geometry than just the metric properties of figures: perspective is the origin of projective geometry. [132] Artists have long used concepts of proportion in design.
Category theory is a unifying theory of mathematics that was initially developed in the second half of the 20th century. [4] In this respect, it is an alternative and complement to set theory. A key theme from the "categorical" point of view is that mathematics requires not only certain kinds of objects ( Lie groups , Banach spaces , etc.) but ...
A diagram of a wheel, as the real projective line with a point at nullity (denoted by ⊥). A wheel is a type of algebra (in the sense of universal algebra) where division is always defined. In particular, division by zero is meaningful. The real numbers can be extended to a wheel, as can any commutative ring.
Linear congruence theorem (number theory, modular arithmetic) Quillen–Suslin theorem (abstract algebra) Rédei's theorem (group theory) Schwartz–Zippel theorem (polynomials) Structure theorem for finitely generated modules over a principal ideal domain (abstract algebra) Unmixedness theorem (algebraic geometry)
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