Null hypothesis correlation matrix is formed as

unit matrix to test the applicability of PCA to data set.

Where [micro] is the plaintext, C is the ciphertext corresponding to [micro], [I.sub.N] is a N -dimensional

unit matrix, R is a random N x m matrix with 0/1 elements, A is m x (n +1) dimension matrix over [Z.sub.q] Note that both R and A are generated by KeyGen() introduced in GSW, so we no longer introduce it in details.

where [R.sub.k+1] is the covariance matrix of the observation noise and the measurement matrix [H.sub.k+1] is a

unit matrix.

Obviously, for [absolute value of z] [right arrow] [infinity], the integral T converges to the

unit matrix. On the other hand we already know from Lemma 4 that

where [[K].sub.L] = [E] + [h/2][[L].sup.-1.sub.ij][[R].sub.ij], [E] is the

unit matrix.

To this end, fix some [mathematical expression not reproducible] is taken large enough such that all diagonal entries of M are positive, and the matrix I is a five-order

unit matrix. In fact, by the hypothetical conditions (H1) and (H2), the directed graph G(M) made of vertices [V.sub.1], [V.sub.2], ..., [V.sub.5] is strongly connected.

where E is the

unit matrix. Hence when N is a sufficiently large positive integer, we have

The linear system x(k + 1) = Ax(k), k = 0, 1, ..., is exponentially stable (i.e., [rho](A) < 1, where [rho] is the spectral radius of A defined by [rho](A) = max{[absolute value of [lambda]]: [lambda] [member of] [sigma](A)}, [sigma](A) := {z [member of] C: det(A - zE) = 0} is the set of all eigenvalues of A, and E is the

unit matrix), if and only if, for an arbitrary positive definite symmetric n x n matrix C, the matrix equation (5) has a unique solution--a positive definite symmetric matrix H ([12, 13]).

We can see that (16) is exactly equivalent to (8) if C is square matrix and W is

unit matrix. The greatest contribution of (16) is to avoid the direct inversion problem when the coefficient matrix is not a square matrix.

If matrix [[PHI].sub.1] is

unit matrix, and [[PHI].sub.2] has good RIP, then [[[PHI].sub.1] | [[PHI].sub.2]] also has good RIP.

where k = (1,2,3) and I is the 2x2

unit matrix. The three 2x2 Pauli spin matrices [[sigma].sub.k] are [1, p.