Random subsets of structured deterministic frames have MANOVA spectra

Random Subsets of Structured Deterministic Frames have MANOVA Spectra

We draw a random subset of [Formula: see text] rows from a frame with [Formula: see text] rows (vectors) and [Formula: see text] columns (dimensions), where [Formula: see text] and [Formula: see text] are proportional to [Formula: see text] For a variety of important deterministic equiangular tight frames (ETFs) and tight non-ETFs, we consider the distribution of singular values of the [Formula...

Spectra of Compact Regular Frames

By Isbell duality, each compact regular frame L is isomorphic to the frame of opens of a compact Hausdorff space X. In this note we study the spectrum Spec(L) of prime filters of a compact regular frame L. We prove that X is realized as the minimum of Spec(L) and the Gleason cover of X as the maximum of Spec(L). We also characterize zero-dimensional, extremally disconnected, and scattered compa...

Structured Group Frames

We introduce and discuss the properties of a new class of finite-dimensional frames with strong symmetry properties called geometrically uniform (GU) frames, that are defined over a finite abelian group of unitary matrices and are generated by a single generating vector. The notion of GU frames is then extended to compound GU (CGU) frames which are generated by a finite abelian group of unitary...

On Random Shuffles & Subsets

Four simple algorithms are presented for producing a random rearrangement of the values in an array X[1], X[2], ..., X[n] using a pseudorandom number generator. These range from one that is naive, inefficient, and biased to one that is elegeant, efficient, and unbiased. By taking the first k entries in X one obtains a random (ordered) subset of size k.

Quasi - Random Subsets of Z