Abstract:
We define the entropy of an orthogonal matrix O/sup i//sub j./ The entropy of the i/sup th/ row can have the maximum value ln n, which is attained when each element of th...Show MoreMetadata
Abstract:
We define the entropy of an orthogonal matrix O/sup i//sub j./ The entropy of the i/sup th/ row can have the maximum value ln n, which is attained when each element of the row is /spl plusmn/1//spl radic/n. This gives the bound, H{O/sup i//sub j/} /spl les/ n ln n. In general, the entropy of an orthogonal matrix cannot attain this bound because of the orthogonality constraint. In fact the bound is obtained only by the Hadamard matrices (rescaled by n/sup - 1/2 /). Thus we have a new criterion for the Hadamard matrices (appropriately normalized): those orthogonal matrices which saturate the bound for entropy.
Published in: Proceedings of the IEEE Information Theory Workshop
Date of Conference: 25-25 October 2002
Date Added to IEEE Xplore: 06 January 2003
Print ISBN:0-7803-7629-3