In this paper, we generalize the definition of fuzzy inner product space that is introduced by Lorena Popa and Lavinia Sida on a complex linear space. Certain properties generalized function are shown. Furthermore, prove produces Nadaban-Dzitac norm. Finally, concept orthogonality given some its proven.

We introduce a simple uniform structure of elementary Φ-unitary matrices. Elementary Φ-unitary transformations are the extentions of Householder transformations in real and complex spaces with a definite or an indefinite inner product induced by a nonsingular signature matrix Φ. The extentions are found useful in the computations of complex matrices or special structured matrices. For two (comp...

1 Dot product of R The inner product or dot product of R is a function 〈 , 〉 defined by 〈u,v〉 = a1b1 + a2b2 + · · ·+ anbn for u = [a1, a2, . . . , an] , v = [b1, b2, . . . , bn] ∈ R. The inner product 〈 , 〉 satisfies the following properties: (1) Linearity: 〈au + bv,w〉 = a〈u,w〉+ b〈v,w〉. (2) Symmetric Property: 〈u,v〉 = 〈v,u〉. (3) Positive Definite Property: For any u ∈ V , 〈u,u〉 ≥ 0; and 〈u,u〉 =...

We reformulate the integrality property of the Poincaré inner product in the middle dimension, for an arbitrary Poincaré Q-algebra, in classical terms (discriminant and local invariants). When the algebra is 1-connected, we show that this property is the only obstruction to realizing it by a closed manifold, up to dimension 11. We reinterpret a result of Eisenbud and Levine on finite map germs,...

Let R be an algebraic curvature tensor for a non-degenerate inner product of signature (p, q) where q ≥ 5. If π is a spacelike 2 plane, let R(π) be the associated skewsymmetric curvature operator. We classify the algebraic curvature tensors so R(·) has constant rank 2 and show these are geometrically realizable by hypersurfaces in flat spaces. We also classify the Ivanov-Petrova algebraic curva...

A collective signature scheme aims to solve the problem of signing a message by multiple signers. Recently, Moldovyan and Moldovyan [1] proposed a scheme for collective signatures based on Schnorr signatures. We show some security weaknesses of the scheme.