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Exact(7)
In the following, let denote the set of real matrices.
R n denotes the n-dimensional Euclidean space and R n × m is the set of real matrices.
In the following, let denote the set of real matrices and let denote the subset of consisting of symmetric matrices.
Throughout this paper, ({{mathrm{R}}^{n}}) denotes the n-dimensional Euclidean space, and ({{mathrm{R}}^{n times m}}) is the set of real matrices.
Throughout this letter, unless otherwise specified, let be the space of -dimensional real column vectors and be the set of real matrices.
Throughout this paper,, and denote the set of real matrices, the subset of consisting of symmetric matrices, and the subset of consisting of nonnegative definite matrices, respectively.
Similar(53)
We denote by the set of orthogonal real matrices and by the set of matrices in which have determinant 1.
It is well known that there exists a positive vector u such that (Au=rho(A)u), u being called the right Perron eigenvector of A. Denote by (Z_{n}) the set of (ntimes{n}) real matrices all of whose off-diagonal entries are nonpositive.
Let be the space of -dimensional (nonnegative) real column vectors, be the set of (nonnegative) real matrices, be the -dimensional unit matrix, and be the Euclidean norm of.
Throughout this paper, and denote, respectively, the -dimensional Euclidean space and the set of all real matrices.
Let (mathcal {B}) denote the set of real symmetric matrices with spectrum σ, mathcal{B} = left{Q in mathbb{R}^{Ntimes N} | Q = P Sigma P^{-1}right}, (9).
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