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Candan introduces [8] matrices whose eigenvectors are higher-order approximations to the Hermite-Gaussian functions.
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The obtained matrix is the DFT-commuting matrix whose eigenvectors are the Hermite-Gaussian-like orthonormal vectors.
This latter is a n × n matrix whose eigenvectors have special meaning.
Matching defines a positive definite 2N2×2N2 matrix Q whose eigenvectors form the orthogonal coordinate functions.
All training images irrespective of class label are used to calculate a covariance matrix C whose eigenvectors define a single PCS.
Pei et al. [7] define a commuting matrix inspired by the work of Grünbaum [13], whose eigenvectors approximate the samples of continuous Hermite-Gaussian functions better than the eigenvectors of.
In this case, the temporal smoothing process is not necessary, and a method for determining the true estimates is formulated as follows: let E n be the 6×4 noise-subspace eigenvector matrix whose four columns are the 6×1 noise-subspace eigenvectors associated with four smallest eigenvalues of ZZ H.
Let E s be the 6P × 2K signal-subspace eigenvector matrix, whose columns are the 6P × 1 signal-subspace eigenvectors associated with the 2K largest eigenvalues of (mathbf {Z}_{text {TS}}mathbf {Z}_{text {TS}}^{H}).
Let be a unitary matrix, whose column vectors are eigenvectors corresponding to, respectively.
where are the three eigenvalues of the matrix H, and U is an orthonormal matrix whose columns are the eigenvectors of matrix H.
where ψ ∗ is a matrix whose rows are left eigenvectors of zero eigenvalue of the matrix D 1 F , 0 ), that is, ψ ∗ D 1 F , 0 ) = 0. (5.2).
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