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].