-
1
-
-
84968518180
-
A theorem on a mapping from a sphere to the circle and the simultaneous diagonalization of two hermitian matrices
-
Y.-H. Au-Yeung A theorem on a mapping from a sphere to the circle and the simultaneous diagonalization of two hermitian matrices, Proc. Amer. Math. Soc., 20 (1969), pp. 545-548.
-
(1969)
Proc. Amer. Math. Soc.
, vol.20
, pp. 545-548
-
-
Au-Yeung, Y.-H.1
-
2
-
-
24644516461
-
Some theorems on simultaneous diagonalization of two Hermitian bilinear functions
-
Y.-H. Au-Yeung, Some theorems on simultaneous diagonalization of two Hermitian bilinear functions, Glasnik Mat., 6 (1971), pp. 3-8.
-
(1971)
Glasnik Mat.
, vol.6
, pp. 3-8
-
-
Au-Yeung, Y.-H.1
-
3
-
-
0002825729
-
A remark on the convexity and positive definiteness concerning Hermitian matrices
-
Y.-H. Au-Yeung and Y. T. Poon, A remark on the convexity and positive definiteness concerning Hermitian matrices, Southeast Asian Bull. Math., 3 (1979), pp. 85-92.
-
(1979)
Southeast Asian Bull. Math.
, vol.3
, pp. 85-92
-
-
Au-Yeung, Y.-H.1
Poon, Y.T.2
-
4
-
-
0003887067
-
-
John Wiley and Sons, Chichester, UK, (translation of the original 1986 Russian edition)
-
T. Ya. Azizov and I. S. Iohvidov, Linear Operators in Spaces with an Indefinite Metric, John Wiley and Sons, Chichester, UK, 1989 (translation of the original 1986 Russian edition).
-
(1989)
Linear Operators in Spaces With an Indefinite Metric
-
-
Azizov, T.Ya.1
Iohvidov, I.S.2
-
5
-
-
0037289010
-
Numerical computation of deflating subspaces of skew-Hamiltonian/ Hamiltonian pencils
-
P. Benner, R. Byers, V. Mehrmann, and H. Xu, Numerical computation of deflating subspaces of skew-Hamiltonian/Hamiltonian pencils, SIAM J. Matrix Anal. Appl., 24 (2002), pp. 165-190.
-
(2002)
SIAM J. Matrix Anal. Appl.
, vol.24
, pp. 165-190
-
-
Benner, P.1
Byers, R.2
Mehrmann, V.3
Xu, H.4
-
6
-
-
0010120775
-
On the field of values of a matrix
-
L. Brinkman, On the field of values of a matrix, Proc. Amer. Math. Soc., 12 (1961), pp. 61-66.
-
(1961)
Proc. Amer. Math. Soc.
, vol.12
, pp. 61-66
-
-
Brinkman, L.1
-
8
-
-
0000865355
-
Sur la reduction canonique des couples de matrices
-
J. Dieudonné, Sur la reduction canonique des couples de matrices, Bull. Soc. Math. France, 74 (1946), pp. 130-146.
-
(1946)
Bull. Soc. Math. France
, vol.74
, pp. 130-146
-
-
Dieudonné, J.1
-
10
-
-
0001641947
-
Über das Vorkommen definiter und semidefiniter Formen in Scharen quadratischer Formen
-
P. Finsler, Über das Vorkommen definiter und semidefiniter Formen in Scharen quadratischer Formen, Comm. Math. Helv., 9 (1937), pp. 188-192.
-
(1937)
Comm. Math. Helv.
, vol.9
, pp. 188-192
-
-
Finsler, P.1
-
11
-
-
0004132473
-
-
Prentice-Hall, Englewood Cliffs, NJ
-
J. N. Franklin, Matrix Theory, Prentice-Hall, Englewood Cliffs, NJ, 1968.
-
(1968)
Matrix Theory
-
-
Franklin, J.N.1
-
13
-
-
0003631756
-
-
revised ed., AMS Chelsea Publishing, Providence, RI, (translation based on the 1941 original)
-
F. R. Gantmacher and M. G. Krein, Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems, revised ed., AMS Chelsea Publishing, Providence, RI, 2002 (translation based on the 1941 original).
-
(2002)
Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems
-
-
Gantmacher, F.R.1
Krein, M.G.2
-
14
-
-
0039579467
-
Spectral analysis of selfadjoint matrix polynomials
-
I. Gohberg, P. Lancaster, and L. Rodman, Spectral analysis of selfadjoint matrix polynomials, Ann. of Math., 112 (1980), pp. 33-71.
-
(1980)
Ann. of Math.
, vol.112
, pp. 33-71
-
-
Gohberg, I.1
Lancaster, P.2
Rodman, L.3
-
15
-
-
0003947818
-
-
Academic Press, New York
-
I. Gohberg, P. Lancaster, and L. Rodman, Matrix Polynomials, Academic Press, New York, 1982.
-
(1982)
Matrix Polynomials
-
-
Gohberg, I.1
Lancaster, P.2
Rodman, L.3
-
16
-
-
0003498640
-
-
Birkhäuser-Verlag, Basel
-
I. Gohberg, P. Lancaster, and L. Rodman, Matrices and Indefinite Scalar Products, Birkhäuser-Verlag, Basel, 1983.
-
(1983)
Matrices and Indefinite Scalar Products
-
-
Gohberg, I.1
Lancaster, P.2
Rodman, L.3
-
17
-
-
0004137069
-
Invariant Subspaces of Matrices with Applications
-
John Wiley, New York
-
I. Gohberg, P. Lancaster, and L. Rodman, Invariant Subspaces of Matrices with Applications, Canad. Math. Soc. Ser. Monogr. Adv. Texts, John Wiley, New York, 1986.
-
(1986)
Canad. Math. Soc. Ser. Monogr. Adv. Texts
-
-
Gohberg, I.1
Lancaster, P.2
Rodman, L.3
-
18
-
-
24644470814
-
Pairs of quadratic forms
-
M. R. Hestenes, Pairs of quadratic forms, Linear Algebra Appl., 1 (1968), pp. 397-407.
-
(1968)
Linear Algebra Appl.
, vol.1
, pp. 397-407
-
-
Hestenes, M.R.1
-
20
-
-
23144444630
-
On the theory of automorphic functions of a matrix variable, II: The classification of hypercircles under the symplectic group
-
L. K. Hua, On the theory of automorphic functions of a matrix variable, II: The classification of hypercircles under the symplectic group, Amer. J. Math, 66 (1944), pp. 531-563.
-
(1944)
Amer. J. Math
, vol.66
, pp. 531-563
-
-
Hua, L.K.1
-
21
-
-
24644514704
-
The singular case of the equivalence of pairs of Hermitian matrices
-
M. H. Ingraham, The singular case of the equivalence of pairs of Hermitian matrices, Bull. Amer. Math. Soc., 40 (1934).
-
(1934)
Bull. Amer. Math. Soc.
, vol.40
-
-
Ingraham, M.H.1
-
22
-
-
23144465852
-
The equivalence of pairs of Hermitian matrices
-
M. H. Ingraham and K. W. Wegner, The equivalence of pairs of Hermitian matrices, Trans. Amer. Math. Soc., 38 (1935), pp. 145-162.
-
(1935)
Trans. Amer. Math. Soc.
, vol.38
, pp. 145-162
-
-
Ingraham, M.H.1
Wegner, K.W.2
-
23
-
-
0004086193
-
-
Akademie-Verlag, Berlin
-
I. S. Iohvidov, M. G. Krein, and H. Langer, Introduction to the Spectral Theory of Operators in Spaces with an Indefinite Metric, Akademie-Verlag, Berlin, 1982.
-
(1982)
Introduction to the Spectral Theory of Operators in Spaces With an Indefinite Metric
-
-
Iohvidov, I.S.1
Krein, M.G.2
Langer, H.3
-
24
-
-
24644445826
-
The Basic Propositions in the Theory of λ-Zones of Stability of a Canonical System of Linear Differential Equations with Periodic Coefficients
-
Birkhäuser-Verlag, Basel, (translation of the 1955 Russian original)
-
M. G. Krein, The Basic Propositions in the Theory of λ-Zones of Stability of a Canonical System of Linear Differential Equations with Periodic Coefficients, Oper. Theory Adv. Appl. 7, Birkhäuser-Verlag, Basel, 1988 (translation of the 1955 Russian original).
-
(1988)
Oper. Theory Adv. Appl.
, vol.7
-
-
Krein, M.G.1
-
25
-
-
0011332753
-
Introduction to the geometry of indefinite J-spaces and to the theory of operators on those spaces
-
(translation of the 1965 Russian original)
-
M. G. Krein, Introduction to the geometry of indefinite J-spaces and to the theory of operators on those spaces, Amer. Math. Soc. Transl., 93 (1970), pp. 103-176 (translation of the 1965 Russian original).
-
(1970)
Amer. Math. Soc. Transl.
, vol.93
, pp. 103-176
-
-
Krein, M.G.1
-
26
-
-
0039614510
-
On some mathematical principles in the linear theory of damped oscillations of continua, I
-
(translation of the 1955 Russian original)
-
M. G. Krein and H. Langer, On some mathematical principles in the linear theory of damped oscillations of continua, I, Integral Equations Operator Theory, 1 (1978), pp. 364-399 (translation of the 1955 Russian original).
-
(1978)
Integral Equations Operator Theory
, vol.1
, pp. 364-399
-
-
Krein, M.G.1
Langer, H.2
-
27
-
-
0000911292
-
On some mathematical principles in the linear theory of damped oscillations of continua, II
-
(translation of the 1955 Russian original)
-
M. G. Krein and H. Langer, On some mathematical principles in the linear theory of damped oscillations of continua, II, Integral Equations Operator Theory, 1 (1978), pp. 539-566 (translation of the 1955 Russian original).
-
(1978)
Integral Equations Operator Theory
, vol.1
, pp. 539-566
-
-
Krein, M.G.1
Langer, H.2
-
30
-
-
0039266531
-
Minimal symmetric factorizations of symmetric real and complex rational matrix functions
-
P. Lancaster and L. Rodman, Minimal symmetric factorizations of symmetric real and complex rational matrix functions, Linear Algebra Appl., 220 (1995), pp. 249-282.
-
(1995)
Linear Algebra Appl.
, vol.220
, pp. 249-282
-
-
Lancaster, P.1
Rodman, L.2
-
31
-
-
24644515683
-
Canonical forms of real skewsymmetric matrix pairs under strict equivalence and congruence
-
to appear
-
P. Lancaster and L. Rodman, Canonical forms of real skewsymmetric matrix pairs under strict equivalence and congruence, Linear Algebra Appl., to appear.
-
Linear Algebra Appl.
-
-
Lancaster, P.1
Rodman, L.2
-
32
-
-
0004293156
-
-
2nd ed., Academic Press, Orlando, FL
-
P. Lancaster and M. Tismenetsky, The Theory of Matrices, 2nd ed., Academic Press, Orlando, FL, 1985.
-
(1985)
The Theory of Matrices
-
-
Lancaster, P.1
Tismenetsky, M.2
-
33
-
-
5544285658
-
Inverse spectral problems for linear and quadratic matrix pencils
-
P. Lancaster and Q. Ye, Inverse spectral problems for linear and quadratic matrix pencils, Linear Algebra Appl., 107 (1988), pp. 293-309.
-
(1988)
Linear Algebra Appl.
, vol.107
, pp. 293-309
-
-
Lancaster, P.1
Ye, Q.2
-
34
-
-
0040253201
-
Variational properties and Rayleigh quotient algorithms for symmetric matrix pencils
-
Birkhäuser-Verlag, Basel
-
P. Lancaster and Q. Ye, Variational properties and Rayleigh quotient algorithms for symmetric matrix pencils, in The Gohberg Anniversary Collection, Vol. I, Oper. Theory Adv. Appl. 40, Birkhäuser-Verlag, Basel, 1989, pp. 247-278.
-
(1989)
The Gohberg Anniversary Collection, Vol. I, Oper. Theory Adv. Appl.
, vol.40
, pp. 247-278
-
-
Lancaster, P.1
Ye, Q.2
-
35
-
-
0039571196
-
Factorization of operator pencils
-
H. Langer, Factorization of operator pencils, Acta Sci. Math. (Szeged), 38 (1976), pp. 83-96.
-
(1976)
Acta Sci. Math. (Szeged)
, vol.38
, pp. 83-96
-
-
Langer, H.1
-
36
-
-
0000902795
-
Canonical forms for Hamiltonian and symplectic matrices and pencils
-
W. W. Lin, V. Mehrmann, and H. Xu, Canonical forms for Hamiltonian and symplectic matrices and pencils, Linear Algebra Appl., 302/303 (1999), pp. 469-533.
-
(1999)
Linear Algebra Appl.
, vol.302-303
, pp. 469-533
-
-
Lin, W.W.1
Mehrmann, V.2
Xu, H.3
-
38
-
-
0004271052
-
-
W. H. Freeman, San Francisco, CA, (translation of the 1948 Russian original)
-
A. I. Malcev, Foundations of Linear Algebra, W. H. Freeman, San Francisco, CA, 1961 (translation of the 1948 Russian original).
-
(1961)
Foundations of Linear Algebra
-
-
Malcev, A.I.1
-
39
-
-
24644481749
-
Pencils of real symmetric matrices and the numerical range
-
M. Marcus, Pencils of real symmetric matrices and the numerical range, Aequationes Math., 17 (1978), pp. 91-103.
-
(1978)
Aequationes Math.
, vol.17
, pp. 91-103
-
-
Marcus, M.1
-
40
-
-
1142307789
-
Canonical forms for doubly structured matrices and pencils
-
C. Mehl, V. Mehrmann, and H. Xu, Canonical forms for doubly structured matrices and pencils, Electron. J. Linear Algebra, 7 (2000), pp. 112-151.
-
(2000)
Electron. J. Linear Algebra
, vol.7
, pp. 112-151
-
-
Mehl, C.1
Mehrmann, V.2
Xu, H.3
-
41
-
-
0037555939
-
Structured Jordan canonical forms for structured matrices that are Hermitian, skew-Hermitian, or unitary with respect to an indefinite inner product
-
V. Mehrmann and H. Xu, Structured Jordan canonical forms for structured matrices that are Hermitian, skew-Hermitian, or unitary with respect to an indefinite inner product, Electron. J. Linear Algebra, 5 (1999), pp. 67-103.
-
(1999)
Electron. J. Linear Algebra
, vol.5
, pp. 67-103
-
-
Mehrmann, V.1
Xu, H.2
-
42
-
-
24644516940
-
Über reele Åquivalenz von Scharen reeler Quadratischer Formen
-
P. Muth, Über reele Åquivalenz von Scharen reeler Quadratischer Formen, Crelle's Journal, 128 (1905) pp. 302-343.
-
(1905)
Crelle's Journal
, vol.128
, pp. 302-343
-
-
Muth, P.1
-
43
-
-
3242705925
-
Über die Spektraldarstellung quadratischer Formen in linearen Räumen mit indefiniter Metrik
-
E. Pesonen, Über die Spektraldarstellung quadratischer Formen in linearen Räumen mit indefiniter Metrik, Ann. Acad. Sci. Fenn. Ser. A., 227 (1956).
-
(1956)
Ann. Acad. Sci. Fenn. Ser. A.
, vol.227
-
-
Pesonen, E.1
-
44
-
-
0038924164
-
Hermitian operators in spaces with indefinite metric
-
L. S. Pontryagin, Hermitian operators in spaces with indefinite metric, Izvestiya Akad. Nauk SSSR, Ser. Matem., 8 (1944), pp. 243-280.
-
(1944)
Izvestiya Akad. Nauk SSSR, Ser. Matem.
, vol.8
, pp. 243-280
-
-
Pontryagin, L.S.1
-
45
-
-
0001399701
-
Minimal factorization of selfadjoint rational matrix functions
-
A. C. M. Ran, Minimal factorization of selfadjoint rational matrix functions, Integral Equations Operator Theory, 5 (1982), pp. 850-869.
-
(1982)
Integral Equations Operator Theory
, vol.5
, pp. 850-869
-
-
Ran, A.C.M.1
-
46
-
-
0000013596
-
Stability of invariant Lagrangian subspaces. I
-
Birkhäuser-Verlag, Basel
-
A. C. M. Ran and L. Rodman, Stability of invariant Lagrangian subspaces. I, in Topics in Operator Theory, Oper. Theory Adv. Appl. 32, Birkhäuser-Verlag, Basel, 1988, pp. 181-218.
-
(1988)
Topics in Operator Theory, Oper. Theory Adv. Appl.
, vol.32
, pp. 181-218
-
-
Ran, A.C.M.1
Rodman, L.2
-
47
-
-
44949291177
-
Stable invariant Lagrangian subspaces: Factorization of symetric rational matrix functions and other applications
-
A. C. M. Ran and L. Rodman, Stable invariant Lagrangian subspaces: Factorization of symmetric rational matrix functions and other applications, Linear Algebra Appl., 137/138 (1990), pp. 575-620.
-
(1990)
Linear Algebra Appl.
, vol.137-138
, pp. 575-620
-
-
Ran, A.C.M.1
Rodman, L.2
-
49
-
-
0003951930
-
-
3rd ed., Dover, New York, (1st ed., 1877)
-
J. W. S. Rayleigh, The Theory of Sound, 3rd ed., Dover, New York, 1945 (1st ed., 1877).
-
(1945)
The Theory of Sound
-
-
Rayleigh, J.W.S.1
-
51
-
-
0004279572
-
-
Springer-Verlag, New York
-
L. Smith, Linear Algebra, Springer-Verlag, New York, 1984.
-
(1984)
Linear Algebra
-
-
Smith, L.1
-
52
-
-
0001750429
-
The characteristic polynomial of a principal subpencil of a Hermitian matrix pencil
-
R. C. Thompson, The characteristic polynomial of a principal subpencil of a Hermitian matrix pencil, Linear Algebra Appl., 14 (1976), pp. 135-177.
-
(1976)
Linear Algebra Appl.
, vol.14
, pp. 135-177
-
-
Thompson, R.C.1
-
53
-
-
0001625882
-
Pencils of complex and real symmetric and skew matrices
-
R. C. Thompson, Pencils of complex and real symmetric and skew matrices, Linear Algebra Appl., 147 (1991), pp. 323-371.
-
(1991)
Linear Algebra Appl.
, vol.147
, pp. 323-371
-
-
Thompson, R.C.1
-
54
-
-
23144450224
-
On the canonical form of a non-singular pencil of Hermitian matrices
-
G. R. Trott, On the canonical form of a non-singular pencil of Hermitian matrices, Amer. J. Math., 56 (1934), pp. 359-371.
-
(1934)
Amer. J. Math.
, vol.56
, pp. 359-371
-
-
Trott, G.R.1
-
55
-
-
84963088619
-
On the equivalence of pencils of Hermitian forms
-
H. W. Turnbull, On the equivalence of pencils of Hermitian forms, Proc. London Math. Soc. (2), 39 (1935), pp. 232-248.
-
(1935)
Proc. London Math. Soc.
, vol.39
, Issue.2
, pp. 232-248
-
-
Turnbull, H.W.1
-
57
-
-
0001175776
-
A recurring theorem about pairs of quadratic forms and extensions: A survey
-
F. Uhlig, A recurring theorem about pairs of quadratic forms and extensions: A survey, Linear Algebra Appl., 25 (1979), pp. 219-237.
-
(1979)
Linear Algebra Appl.
, vol.25
, pp. 219-237
-
-
Uhlig, F.1
-
59
-
-
23144465852
-
The equivalence of pairs of Hermitian matrices
-
K. W. Wegner, The equivalence of pairs of Hermitian matrices, Trans. Amer. Math. Soc., 38 (1935), pp. 145-162.
-
(1935)
Trans. Amer. Math. Soc.
, vol.38
, pp. 145-162
-
-
Wegner, K.W.1
-
60
-
-
0011039516
-
Zur Theorie der quadratischen und bilinearen Formen
-
Berlin
-
K. Weierstrass, Zur Theorie der quadratischen und bilinearen Formen, Monatsber. Akad. Wiss., Berlin, 1868, pp. 310-338.
-
(1868)
Monatsber. Akad. Wiss.
, pp. 310-338
-
-
Weierstrass, K.1
-
61
-
-
23144442204
-
The equivalence of nonsingular pencils of Hermitian matrices in an arbitrary field
-
J. Williamson, The equivalence of nonsingular pencils of Hermitian matrices in an arbitrary field, Amer. J. Math., 57 (1935), pp. 475-490.
-
(1935)
Amer. J. Math.
, vol.57
, pp. 475-490
-
-
Williamson, J.1
-
62
-
-
0001316020
-
On the algebraic problem concerning the normal forms of linear dynamical systems
-
J. Williamson, On the algebraic problem concerning the normal forms of linear dynamical systems, Amer. J. Math., 58 (1936), pp. 141-163.
-
(1936)
Amer. J. Math.
, vol.58
, pp. 141-163
-
-
Williamson, J.1
-
63
-
-
23144442447
-
Note on the equivalence of nonsingular pencils of Hermition matrices
-
J. Williamson, Note on the equivalence of nonsingular pencils of Hermition matrices, Bull. Amer. Math. Soc., 51 (1945), pp. 894-897.
-
(1945)
Bull. Amer. Math. Soc.
, vol.51
, pp. 894-897
-
-
Williamson, J.1
|