We exhibit equivalent conditions for subspaces of an inner product space to be isoclinic, including a characterization based on the classical notion canonical angles. identify connection with quantum error correction, showing that every correcting code is associated family isoclinic subspaces, and we prove converse pairs such subspaces. also show how angles arise in structure higher rank numeri...

This paper introduces a new method to solve the cross-domain recognition problem. Different from the traditional domain adaption methods which rely on a global domain shift for all classes between source and target domain, the proposed method is more flexible to capture individual class variations across domains. By adopting a natural and widely used assumption – “the data samples from the same...

‎In this paper‎, ‎we characterize the class of orthogonality preserving operators on an infinite-dimensional Hilbert space $H$ as scalar multiples of unitary operators between $H$ and some closed subspaces of $H$‎. ‎We show that any circle (centered at the origin) is the spectrum of an orthogonality preserving operator‎. ‎Also‎, ‎we prove that every compact normal operator is a strongly orthogo...

Subspace clustering is the problem of clustering data that lie close to a union of linear subspaces. Existing algebraic subspace clustering methods are based on fitting the data with an algebraic variety and decomposing this variety into its constituent subspaces. Such methods are well suited to the case of a known number of subspaces of known and equal dimensions, where a single polynomial van...

We establish the connection between decoherence-free subspaces of quantum information and spontaneous emission cancellation in quantum optics with molecules. Both phenomena rely on the destructive interference of transition amplitudes from two initial states to a common target state. We discuss physical similarities, differences, and limitations of both phenomena.

In the paper titled “Lattices generated by two orbits of subspaces under finite classical group” byWang andGuo.The subspaces in the lattices are characterized and the geometricity is classified. In this paper, the result above is generalized to singular symplectic space. This paper characterizes the subspaces in these lattices, classifies their geometricity, and computes their characteristic po...

A correlation analysis will be applied to subspaces of the t-ness landscape generated by the synchronization task for one-dimensional cellular automata. This results in a stochastic model that can be used to characterize the correlation structure of those subspaces. The results show that both subspaces can be characterized by an AR(2) model, both for point mutation and crossover.

In this paper we consider translation and dilation invariant subspaces of C(IR). We characterize all such subspaces and also identify those f ∈ C(IR), the span of whose translates and dilates generate non-trivial subspaces. We apply these and related results to some mathematical models in the theory of neural networks. §

Let T be a self-adjoint operator acting in a separable Hilbert space H. We establish a correspondence between the reducing subspaces of T that come from a spectral projection and the convex, norm-closed bands in the set of finite Borel measures on R. IfH is not separable, we still obtain a reducing subspace corresponding to each convex norm-closed band. These observations lead to a unified trea...

Suppose $G$ is a split connected‎ ‎reductive orthogonal or symplectic group over an infinite field‎ ‎$F,$ $P=MN$ is a maximal parabolic subgroup of $G,$ $frak{n}$ is‎ ‎the Lie algebra of the unipotent radical $N.$ Under the adjoint‎ ‎action of its stabilizer in $M,$ every maximal prehomogeneous‎ ‎subspaces of $frak{n}$ is determined‎.