On the Sum of the Largest Eigenvalues of a Symmetric Matrix Rev Ed
On the Sum of the Largest Eigenvalues of a Symmetric Matrix Rev Ed
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Our approach provides a very convenient characterization for the subdifferential of the eigenvalue sum, to be described in a subsequent paper.
Let yl be an n by n real symmetric matrix, with eigenvalues Ai > •••> A„ and a corresponding orthonormal set of eigenvectors qi, . . . , Qn', thus A = Q\Q'^, Q^Q = In, where A = Diag(Ai, . . . , A„) and Q = [91, ... , 9„]. In 1949, the following theorem was proved by Ky Fan [Fan]: 'Computer Science Department, Courant Institute of Mathematical Sciences, ...New York University. The work of this author was supported in part by National Science Foundation Grant CCR-88-02408.
'School of Mathematics, University of New South Wales. The work of this author was supported in part by U. S. Department of Energy Contract DEFG0288ER25053 during a visit to New York University.
Theorem 1 E A, = max trA'MA'. (1) Here Ik is the identity matrix of order k, and hence A' is a matrix whose columns are k orthonormal vectors in 3f?". (AH matrices are assumed to be real, but extension to the case where A is complex Hermitian is straightfor- ward.
What to read after On the Sum of the Largest Eigenvalues of a Symmetric Matrix Rev Ed?
You can find similar books in the "Read Also" column, or choose other free books by Micheal L Overton to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Our approach provides a very convenient characterization for the subdifferential of the eigenvalue sum, to be described in a subsequent paper.
Let yl be an n by n real symmetric matrix, with eigenvalues Ai > •••> A„ and a corresponding orthonormal set of eigenvectors qi, . . . , Qn', thus A = Q\Q'^, Q^Q = In, where A = Diag(Ai, . . . , A„) and Q = [91, ... , 9„]. In 1949, the following theorem was proved by Ky Fan [Fan]: 'Computer Science Department, Courant Institute of Mathematical Sciences, ...New York University. The work of this author was supported in part by National Science Foundation Grant CCR-88-02408.
'School of Mathematics, University of New South Wales. The work of this author was supported in part by U. S. Department of Energy Contract DEFG0288ER25053 during a visit to New York University.
Theorem 1 E A, = max trA'MA'. (1) Here Ik is the identity matrix of order k, and hence A' is a matrix whose columns are k orthonormal vectors in 3f?". (AH matrices are assumed to be real, but extension to the case where A is complex Hermitian is straightfor- ward.
What to read after On the Sum of the Largest Eigenvalues of a Symmetric Matrix Rev Ed?
You can find similar books in the "Read Also" column, or choose other free books by Micheal L Overton to read onlineMoreLess
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