Sivaram K. Narayan

Learn More
We consider frames in a finite-dimensional Hilbert space H n where frames are exactly the spanning sets of the vector space. The diagram vector of a vector in R 2 was previously defined using polar coordinates and was used to characterize tight frames in R 2 in a geometric fashion. Reformulating the definition of a diagram vector in R 2 we provide a natural(More)
A tight frame in R<sup>n</sup> is a redundant system which has a reconstruction formula similar to that of an orthonormal basis. For a unit-norm frame F = {f<sub>i</sub>}<sup>k</sup><sub>i=1</sub>, a scaling is a vector c = (c(l),..., c(k)) &#x03B5; R<sup>k</sup>&#x2265;0 such that {c(i)f<sub>i</sub>}<sup>k</sup><sub>i=1</sub> is a tight frame in(More)
Let G = (V, E) be a multigraph with no loops on the vertex set V = {1, 2,. .. , n}. Define S + (G) as the set of symmetric positive semidefinite matrices A = [a ij ] with a ij = 0, i = j, if ij ∈ E(G) is a single edge and a ij = 0, i = j, if ij / ∈ E(G). Let M + (G) denote the maximum multiplicity of zero as an eigenvalue of A ∈ S + (G) and mr + (G) = |G| −(More)
A magic square M is an n-by-n array of numbers whose rows, columns, and the two diagonals sum to µ called the magic sum. If all the diagonals including broken diagonals sum to µ then the magic square is said to be pandiagonal. A regular magic square satisfies the condition that the entries symmetrically placed with respect to the center sum to 2µ n. If the(More)
  • 1