holds, and it actually holds for any
normal matrix A.
Since is a
normal matrix, there exists a unitary matrix such that
With calculation of k value and its multiply in correlation matrix, the
normal matrix, table(6) is formed.
Then, we show that any real matrix can be made arbitrarily close to a
normal matrix by a series of similarity transformations, based on which our proposed algorithm can be extended to the case of arbitrary real matrices.
From Theorem 2.1 (iii), the
normal matrix [R.sub.??]] - [L.sub.[??]] has the same eigenvalues as [R.sub.[??]] - [L.sub.[??]] and therefore the same rank.
Throughout this paper we assume that [lambda] = ([[lambda].sub.k]) and [mu] = ([[mu].sub.k]) are sequences with 0 < [[lambda].sub.k]; [[mu].sub.k] [??] [??] [infinity]; A is a
normal matrix with its inverse matrix [A.sup.-1] = ([[eta].sub.kl]); B = ([b.sub.nk]) is a triangular matrix, and M = ([m.sub.nk]) is an arbitrary matrix.
To speed up the convergence when solving the low-order minimization problem, we use a preconditioned global conjugate gradient method associated to the
normal matrix equation.
In the above formula, Frequency [f.sub.k] is k-th normal mode structures, [M] is structural mass matrix and [{[phi]}.sub.k] is eigenvector curvature of k-th vibration mode shape that with multiplying this matrix and the
normal matrix transpose the mass of it is used in the following equation.
Therefore, if we decompose the unique normal traffic into two matrices, we can obtain
normal matrix uniquely.
He gave a necessary and sufficient condition that characterize the set of k complex values occurring as Ritz values of a given
normal matrix. Carden and Hansen [7] also gave a condition that is equivalent to Bujanovic's.
The properties of a
normal matrix can be accurately predicted by its spectrum.