Tight frames, Hadamard matrices and Zauner’s conjecture

tight frame approximation for multi-frames and super-frames

در این پایان نامه یک مولد برای چند قاب یا ابر قاب تولید شده تحت عمل نمایش یکانی تصویر برای گروه های شمارش پذیر گسسته بررسی خواهد شد. مثال هایی از این قاب ها چند قاب های گابور، ابرقاب های گابور و قاب هایی برای زیرفضاهای انتقال پایاست. نشان می دهیم که مولد چند قاب تنک نرمال شده (ابرقاب) یکتا وجود دارد به طوری که مینیمم فاصله را از ان دارد. همچنین مسایل مشابه برای قاب های دوگان مطرح شده و برخی ...

Complex Hadamard Matrices and the Spectral Set Conjecture

By analyzing the connection between complex Hadamard matrices and spectral sets we prove the direction “spectral ⇒ tile” of the Sectral Set Conjecture for all sets A of size |A| ≤ 5 in any finite Abelian group. This result is then extended to the infinite grid Z for any dimension d, and finally to R. It was pointed out recently in [16] that the corresponding statement fails for |A| = 6 in the g...

Jacket matrices constructed from Hadamard matrices and generalized Hadamard matrices

Hadamard and Conference Matrices

We discuss new constructions of Hadamard and conference matrices using relative difference sets. We present the first example of a relative (n, 2, n − 1, n−2 2 )-difference set where n − 1 is not a prime power.

Entropy and Hadamard Matrices

The entropy of an orthogonal matrix is defined. It provides a new interpretation of Hadamard matrices as those that saturate the bound for entropy. It appears to be a useful Morse function on the group manifold. It has sharp maxima and other saddle points. The matrices corresponding to the maxima for 3 and 5 dimensions are presented. They are integer matrices (upto a rescaling.)