by X ⊗ ι Y {\displaystyle X\otimes _{\iota }Y} and called the inductive tensor product of X {\displaystyle X} and Y . {\displaystyle Y.} Throughout let...

topological tensor product of two topological vector spaces. For Hilbert spaces or nuclear spaces there is a simple well-behaved theory of tensor products (see...

projective tensor product of two locally convex topological vector spaces is a natural topological vector space structure on their tensor product. Namely...

product of Hilbert spaces – Tensor product space endowed with a special inner product Topological tensor product – Tensor product constructions for topological...

topology Inductive tensor product Injective tensor product Projective tensor product Tensor product of Hilbert spaces Topological tensor product Émery topology...

injective tensor product is a particular topological tensor product, a topological vector space (TVS) formed by equipping the tensor product of the underlying...

Induction cooking Induction motors Induction sealing Induction welding Inductive charging Inductors Magnetic flow meters Mechanically powered flashlight...

_{1}\right)} is nuclear, this tensor product is simultaneously the injective tensor product and projective tensor product). In short, the Schwartz kernel...

Direct sum and the dual construction product Subspace and the dual construction quotient Topological tensor product Discrete space Locally constant function...

the group of units of the ring Z, which is ({−1, +1}, ×) ≅ C2. The tensor product Z/mZ ⊗ Z/nZ can be shown to be isomorphic to Z / gcd(m, n)Z. So we can...

a new direction. The inductive dimension of a topological space may refer to the small inductive dimension or the large inductive dimension, and is based...

{\displaystyle X} is compact, T0, and zero-dimensional (in the sense of the small inductive dimension); X {\displaystyle X} is coherent and Hausdorff. Important examples...

limits and inductive limits exist in the categories of left and right modules. Over a commutative ring, together with the tensor product of modules ⊗...

derived category). tensor category Usually synonymous with monoidal category (though some authors distinguish between the two concepts.) tensor triangulated...

square root of the product of a quaternion with its conjugate is called its norm and is denoted ‖q‖ (Hamilton called this quantity the tensor of q, but this...

f 1 = ⋯ = f r = 0 {\displaystyle f_{1}=\cdots =f_{r}=0} . It is the tensor product of the r many Koszul complexes for f i = 0 {\displaystyle f_{i}=0} ...

"direct inductive limit", "directed colimit", "direct colimit" and "inductive limit" for the concept of direct limit defined above. The term "inductive limit"...

symbolic/knowledge-based learning did continue within AI, leading to inductive logic programming(ILP), but the more statistical line of research was...

identifies three main families of models: tensor decomposition models, geometric models, and deep learning models. The tensor decomposition is a family of knowledge...

integration is a process that finds the integral of a product of functions in terms of the integral of the product of their derivative and antiderivative. It is...

physical law derived from empirical observations by what Isaac Newton called inductive reasoning. It is a part of classical mechanics and was formulated in Newton's...

assumption for covariate information. Objective randomization allows properly inductive procedures. Many statisticians prefer randomization-based analysis of...

curvature two-form Ω. The form F is sometimes referred to as the field strength tensor, in analogy to the role it plays in electromagnetism. Note that D2 vanishes...

Incremental decision tree Induction of regular languages Inductive bias Inductive probability Inductive programming Influence diagram Information Harvesting...

{\displaystyle q=0} . The given tensor products only have pure tensors. Therefore, it suffices to show that if a pure tensor m ⊗ q {\displaystyle m\otimes...

spaces. They play a considerable part in the theory of topological tensor products. DF-spaces were first defined by Alexander Grothendieck and studied...

{\displaystyle g} is everywhere zero, but f g {\displaystyle fg} is. The tensor product C ⊗ R C {\displaystyle \mathbb {C} \otimes _{\mathbb {R} }\mathbb {C}...

T(L) → U(L) of algebras, where T(L) is the tensor algebra on L (for example, by the universal property of tensor algebras), and this is a filtered map equipping...

an inductive current involving spin. There is no linear motion in the inductive current along the direction of the B vector. The magnetic inductive current...

{\displaystyle X} is the inductive limit of a family of nuclear DF-spaces, spanning X . {\displaystyle X.} The finite product of locally convex ultrabornological...