Mathematics and statistics

Tautology (logic)

In logic, a tautology, also known as a logical tautology, is a formula true under every possible interpretation, with p ∨ ¬p the standard example.

Taxicab geometry

Taxicab geometry, also called the Manhattan or city block metric, replaces Euclidean distance with the sum of coordinate differences, making a circle a square and π equal 4.

Taylor model

A Taylor model is a verified-computing representation of a function as a truncated Taylor polynomial plus an interval remainder, giving rigorous bounds on function values and floating-point errors.

Taylor series

The Taylor series, also called the Taylor expansion, represents a function as an infinite sum built from its derivatives at a point; centered at 0, it is a Maclaurin series.

Taylor's theorem

Taylor's theorem, also known as Taylor's formula, is a calculus result approximating a differentiable function near a point by a polynomial, with a bound on the error.

Teichmüller space

Teichmüller space is the space of marked complex or hyperbolic structures on a fixed topological surface, the simply connected marked version of the moduli space of Riemann surfaces.

Temperley–Lieb algebra

The Temperley–Lieb algebra TL_n(δ) is a family of finite-dimensional algebras introduced by Temperley and Lieb in 1971, central to statistical mechanics, knot theory, and quantum groups.

Temporal discretization is the numerical technique of replacing time derivatives in differential equations with difference quotients at discrete time steps, so time-dependent equations can be solved by iterating an update formula.

Temporal logic

Temporal logic is a formal logic extending propositional or first-order logic with operators about time, such as "always" and "eventually", used to specify reactive systems.

Temporal logic of actions

The temporal logic of actions (TLA) is a temporal logic invented by Leslie Lamport in the late 1980s, in which actions may appear directly inside temporal formulas.

Temporally weighted regression

Temporally weighted regression (TWR) is a local regression method that weights observations by their distance in time, addressing temporal nonstationarity, where relationships change over the study period.

Tense logic

Tense logic is a modal-style formalism for reasoning about time, introduced by Arthur Prior in the 1950s; it grew into temporal logic, now standard in computing and verification.

Tensor

A tensor, sometimes called a tensor on a vector space, is a geometric or algebraic object generalizing scalars, vectors, and matrices; the word was introduced by Woldemar Voigt in 1898.

Tensor algebra

The tensor algebra T(V) of a vector space V is the algebra of all tensors on V, with the tensor product as multiplication; it is the free associative algebra on V.

Tensor contraction

Tensor contraction is an operation in multilinear algebra that pairs an upper and lower index of a tensor and sums over it, lowering the tensor's order.

Oct 22, 2026

Tensor cross interpolation

Tensor cross interpolation, also known as TT-cross, is a family of algorithms that compresses high-dimensional tensors into tensor trains by sampling a small subset of their elements.

Tensor factorization

Tensor factorization decomposes a multiway array (tensor) into lower-dimensional component factors for dimensionality reduction and latent-structure recovery; its two central models, CP and Tucker, generalize the matrix singular value decomposition.

Tensor field

A tensor field is a mathematical object that assigns a tensor to each point of a space or manifold, so quantities such as stress vary from point to point.

Tensor network

A tensor network is a factorization of a very large tensor into smaller tensors connected by shared indices, used to represent quantum many-body states compactly.

Tensor product

The tensor product is a construction in multilinear algebra combining two or more vector spaces into a new space V ⊗ W, converting bilinear maps into ordinary linear maps.

Tensor product of algebras

The tensor product of algebras combines two algebras over a common base ring into one algebra, the standard way of making two structures act side by side.

Tensor product of modules

The tensor product of modules takes two modules over a ring R and produces a module M ⊗R N that converts bilinear maps into linear ones.

Tensor rank

Tensor rank is the smallest number of rank-one tensors summing to a given tensor, the order-3-and-higher generalization of matrix rank that is NP-hard to compute.

Tensor rank decomposition

Tensor rank decomposition, also known as the CP decomposition, expresses a tensor as a sum of rank-one tensors; the minimum number of terms is its tensor rank.

Tensor software

Tensor software is software for creating, storing, and computing with tensors, spanning array libraries, decomposition toolboxes like Tensor Toolbox and TensorLy, and tensor network libraries.

Tensor train decomposition

The tensor train decomposition, also known as the matrix product state, represents a high-dimensional tensor as a chain of small three-dimensional cores with linear storage.

Tensor–hom adjunction

The tensor–hom adjunction is a theorem of module theory giving a natural isomorphism Hom(M ⊗ N, P) ≅ Hom(M, Hom(N, P)); it underlies closed monoidal categories and homological algebra.

Tent map

The tent map is a piecewise linear map of the unit interval whose graph rises to a peak at 1/2 and falls back, a simple example of chaos.

Term (logic)

In logic, a term is a first-order logic expression, such as a variable, constant, or function application, that refers to an object in the domain of discourse.