Let A [member of] [R.sup.nxn] be a large,

symmetric matrix, and let V [member of] [R.sup.nxs] be a block vector with 1 [less than or equal to] s << n.

In the associated

symmetric matrix [F'.sub.i] of central map, every column looks random.

(i) An n x n matrix A is called a

symmetric matrix if [A.sup.T] = A.

It found that, for many customers, its standard off-the-shelf

symmetric matrix did not efficiently fit the asymmetric configurations that the customer often required.

where t [greater than or equal to] 0, [tau] is a positive constant fixed delay, x is an n-vector, n [greater than or equal to] 1, A is an n x n-symmetric matrix, H : [R.sup.n] [right arrow] [R.sup.n] is a continuous function with H(0) = 0, C(t, s) is an n x n-continuous

symmetric matrix function for 0 [less than or equal to] s [less than or equal to] t < [infinity], G, E : [R.sup.+] x [R.sup.n] [right arrow] [R.sup.n] are continuous functions with G(t, 0) = 0, and [K.sup.+] = [0, [infinity]).

where ([R.sup.T.sub.d] R - [R.sup.T] [R.sub.d]) [member of] so(3) is a skew-

symmetric matrix, [().sup.v] is the inverse mapping of the hat mapping [().sup.^].

Therefore [[alpha].sub.ij] (x) is a

symmetric matrix:

If A is a real

symmetric matrix, then the condition number of A is

It is well known that the eigenvalues of a real

symmetric matrix are not everywhere differentiable.

For any positive definite

symmetric matrix N [member of] [R.sup.nxn], scalar [tau] > 0, and a vector function x(*) : [-[tau], 0] [right arrow] [R.sup.n], the following integral inequality is satisfied:

The

symmetric matrix F is of low rank, and it is the special structure of the

symmetric matrix F that makes the original HFE scheme insecure.

Matrix A [member of] [R.sup.nxn] is called a

symmetric matrix if A = [A.sup.T].