A. Horn, On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. J. Math., 76(1954), 4-7. 14 Home/Search Document Not in Database Summary Related Articles Check |
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Induced Operators on Symmetry Classes of Tensors - Li, Zaharia (Correct)
....induced operators as shown in later chapters. We present some preliminary lemmas in 2.1. Then we identify special types of characters in 2.2 for which (I) III) may fail. Complete solutions of our problems in connections with (I) III) will be given in 2.3. The first lemma is due to Horn [22] and Weyl [57] Lemma 2.2 Suppose ,1, n are complex numbers with Ill and Sl Sn are nonnegative real numbers. Then there exists A Mwith singular values Sl, s,and eigenvaIues hi, Amif and only if ljn l I Jl : ljn l Sj and j=l j=l fork= l, n 1. The next lemma can be found in ....
A. Horn, On the eigenvalues of a matrix with prescribed singular values,
On the decay rate of Hankel singular values and related issues - Antoulas, Zhou (2002) (3 citations) (Correct)
....b 2 b n ] T 2 C n . In this case the solution of the Lyapunov equation AP PA BB = 0 is precisely the Cauchy matrix scaled by B: C i;j = b i b j i j . Because of the above mentioned fact on the L D U factorization we have the following result due to Alfred Horn [13]; it states that the vector of eigenvalues of a positive de nite matrix majorizes multiplicatively the vector whose i th entry is the quotient of the determinants of the i th over the (i 1) st principal minors of the matrix. Lemma 4.3 Let P be the solution to the Lyapunov equation with ....
A. Horn, On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. Math. Soc., 5: 4-7 (1954).
Construction of Matrices With Prescribed Singular Values and .. - Chi-Kwong Li And (Correct)
....matrices and rotation matrices. It is numerically stable and may be useful in developing test software for numerical linear algebra packages. Keywords: Singular value, Eigenvalue, Majorization AMS(MOS) subject classification: 15A18, 15A99 1 Introduction A classical result of Weyl [9] and Horn [5] completely determines the relations between the singular values and eigenvalues of an n Theta n complex matrix as follows. Theorem 1.1 There exists an n Theta n complex matrix with singular values s 1 Delta Delta Delta s n 0 and eigenvalues 1 ; n 2 C such that j 1 j Delta ....
....jj = kxk = kAxk maxfkAyk : kyk = 1g = s 1 ; and then apply the result to the compound matrices C k (A) for k = 1; n (see [7, 9.E.1] 2, II.3.6] Alternatively, one can use the Schur triangular form (see [6, Theorem 3.3. 2] The sufficiency part is usually not presented in textbooks ([2, 5, 7]) A. Horn s original proof was by induction, and proved the special case where i 6= 0 for all i first, and then extended it to the general case using an idea of Kaplansky [5] Horn s algorithm always generated a matrix with diagonal entries ordered in decreasing absolute value. In this note, two ....
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A. Horn, On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. Math. Soc. 5 (1954), 4--7.
Induced Operators on Symmetry Classes of Tensors - Li, Zaharia (Correct)
....in later chapters. We present some preliminary lemmas in x2.1. Then we identify special types of characters in x2.2 for which (I) III) may fail. Complete solutions of our problems in connections with (I) III) will be given in x2.3. x2.1 Preliminary Lemmas The first lemma is due to Horn [22] and Weyl [57] Lemma 2.2 Suppose 1 ; n are complex numbers with j 1 j Delta Delta Delta j n j, and s 1 Delta Delta Delta s n are nonnegative real numbers. Then there exists A 2 M n with singular values s 1 ; s n and eigenvalues 1 ; n if and only if Q n j=1 j ....
A. Horn, On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. Math. Soc. 5 (1954), 4-7. 46
Spectral Characterization Of Sums Of Commutators Ii - Dykema And (1997) (Correct)
....complex numbers with j 1 j j 2 j Delta Delta Delta and such that j 1 : n j s 1 : s n for all n: Then there is an upper triangular operator A = a jk ) j;k such that s n (A) s n for all n and a jj = j for all j: Proof. This is the infinite dimensional extension of a result of Horn [3] (see Gohberg Krein [2] Remark II.3.1) By Horn s result we can find for each n an upper triangular matrix A (n) a (n) jk ) such that a (n) jk = 0 if max(j; k) n, a n jj = j for 1 j n and s j (A (n) s j for 1 j 1: Now we can pass to a subsequence (B (n) of (A ....
A. Horn, On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. Math. Soc. 5 (1954), 4-7.
On the Optimal Spectral Abscissa for a System of Linear.. - Freitas, Lancaster (1998) (Correct)
....to saying that there exists a real upper triangular n Theta n matrix J with an eigenvalue at Gammaff with multiplicity n and whose singular values are the square roots of the eigenvalues of C. In order to show that such a matrix exists, we shall make use of the following result of A. Horn [H]. See also the discussion of these inequalities in [HJ] Theorem 3.4 [Horn] Let (oe 1 ; Delta Delta Delta ; oe n ) 2 R I n and (ff 1 ; Delta Delta Delta ; ff n ) 2 CI n be a pair of n Gammatuples satisfying jff 1 j Delta Delta Delta jff n j; oe 1 Delta Delta Delta oe n 0 ....
A. Horn, On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. Math. Soc. 5 (1954), 4--7.
SINGULAR VALUE REASSIGNMENT WITH LOW RANK MATRICES (DRAFT.. - Delin Chu And (Correct)
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A. Horn, On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. J. Math., 76(1954), 4-7. 14
A Fast Recursive Algorithm For - Constructing Matrices With (Correct)
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A. Horn, On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. J. Math., 76(1954), 4-7.
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