-
1
-
-
0040929786
-
On the Wishart distribution in statistics
-
A.C. Aitken, On the Wishart distribution in statistics. Biometrika 36 (1949), 59–62.
-
(1949)
Biometrika
, vol.36
, pp. 59-62
-
-
Aitken, A.C.1
-
2
-
-
84947517705
-
Studies on the estimation of variance components
-
Ph.D. Thesis, Cornell University, 136 pp
-
R.D. Anderson, Studies on the estimation of variance components. Ph.D. Thesis, Cornell University 1978. 136 pp.
-
(1978)
-
-
Anderson, R.D.1
-
3
-
-
84891686477
-
Fourth moments in the general linear model; and the variance of translation invariant quadratic forms
-
Paper No. BU-630-M in the Biometrics Unit Mimeo Series, Cornell University, 11 pp
-
R.D. Anderson, R.L. Quaas and S.R. Searle, Fourth moments in the general linear model; and the variance of translation invariant quadratic forms. Paper No. BU-630-M in the Biometrics Unit Mimeo Series, Cornell University (1977). 11 pp.
-
(1977)
-
-
Anderson, R.D.1
Quaas, R.L.2
Searle, S.R.3
-
4
-
-
30244438799
-
-
Collection de l'Institut de Mathématiques Economiques, No. 12, Sirey, Paris
-
Balestra, P. La Dérivation Matricielle. Collection de l'Institut de Mathématiques Economiques, No. 12, Sirey, Paris 1976.
-
(1976)
La Dérivation Matricielle
-
-
Balestra, P.1
-
5
-
-
0348059418
-
Matrix differential equations and Kronecker products
-
S. Barnett, Matrix differential equations and Kronecker products. SIAM J, Appl. Math. 24 (1973), 1–5.
-
(1973)
SIAM J, Appl. Math.
, vol.24
, pp. 1-5
-
-
Barnett, S.1
-
7
-
-
0004178623
-
-
Simon and Schuster, New York
-
E.T. Bell, Men of Mathematics. Simon and Schuster, New York (1937).
-
(1937)
Men of Mathematics
-
-
Bell, E.T.1
-
8
-
-
79951621800
-
Some extensions of matrix calculus
-
P.M. Bentler and Sik-Yum Lee, Some extensions of matrix calculus. General Systems 20 (1975), 145–150.
-
(1975)
General Systems
, vol.20
, pp. 145-150
-
-
Bentler, P.M.1
Lee, S.-Y.2
-
9
-
-
0017747895
-
The derivative of the Ricatti Matrix with respect to a matrix
-
John W. Brewer, The derivative of the Ricatti Matrix with respect to a matrix. IEEE Trans. Automat. Contr. AC-22 (1977), 980–983.
-
(1977)
IEEE Trans. Automat. Contr. AC-22
, pp. 980-983
-
-
Brewer, J.W.1
-
10
-
-
0018011435
-
Kronecker products and matrix calculus in system theory
-
John W. Brewer, Kronecker products and matrix calculus in system theory. IEEE Trans. Cir. Syst. CAS-25 (1978), 772–781.
-
(1978)
IEEE Trans. Cir. Syst.
, vol.CAS-25
, pp. 772-781
-
-
Brewer, J.W.1
-
11
-
-
0001963735
-
Generalized least squares estimators in the analysis of covariance structures
-
M.W. Browne, Generalized least squares estimators in the analysis of covariance structures. South African Statist. J. 8 (1974), 1–24.
-
(1974)
South African Statist. J.
, vol.8
, pp. 1-24
-
-
Browne, M.W.1
-
12
-
-
84947516973
-
Multivariate analysis of variance using patterned covariance matrices
-
Ph.D. Thesis, University of North Carolina, 303 pp
-
J.W.L. Cole, Multivariate analysis of variance using patterned covariance matrices. Ph.D. Thesis, University of North Carolina (1969). 303 pp.
-
(1969)
-
-
Cole, J.W.L.1
-
13
-
-
84947371568
-
The equilibrium covariance matrix of dynamic econometric models
-
J. Conlisk, The equilibrium covariance matrix of dynamic econometric models. J. Amer. Statist. Assoc. 64 (1969), 277–279.
-
(1969)
J. Amer. Statist. Assoc.
, vol.64
, pp. 277-279
-
-
Conlisk, J.1
-
14
-
-
0000901886
-
A further note on stability in a random coefficients model
-
J. Conlisk, A further note on stability in a random coefficients model. Internat. Econom. Rev. 17 (1976), 759–764.
-
(1976)
Internat. Econom. Rev.
, vol.17
, pp. 759-764
-
-
Conlisk, J.1
-
15
-
-
84947528370
-
Multivariate normal estimation with missing data on several variates
-
Trans. 1974 European Meeting of Statisticians, Prague. (1974)
-
M. A. Giguère and G. P. H. Styan, Multivariate normal estimation with missing data on several variates. Trans. 1974 European Meeting of Statisticians, Prague. (1974).
-
-
-
Giguère, M.A.1
Styan, G.P.H.2
-
17
-
-
0003609228
-
-
(Second edition.) D. Van Nostrand Company, Princeton, New Jersey
-
Paul R. Halmos, Finite-dimensional Vector Spaces. (Second edition.) D. Van Nostrand Company, Princeton, New Jersey (1958).
-
(1958)
Finite-dimensional Vector Spaces
-
-
Halmos, P.R.1
-
18
-
-
84909777131
-
The resultant and the matrix equation AX = XB
-
Robert E. Hartwig, The resultant and the matrix equation AX = XB. SIAM J. Appl. Math. 22 (1972), 538–544.
-
(1972)
SIAM J. Appl. Math.
, vol.22
, pp. 538-544
-
-
Hartwig, R.E.1
-
19
-
-
0016435878
-
AX−XB = C, resultants and generalized inverses
-
R.E. Hartwig, AX−XB = C, resultants and generalized inverses. SIAM J. Appl. Math. 28 (1975), 154–183.
-
(1975)
SIAM J. Appl. Math.
, vol.28
, pp. 154-183
-
-
Hartwig, R.E.1
-
20
-
-
84972562546
-
The universal flip matrix and the generalized faro-shuffle
-
R.E. Hartwig and S.B. Morris, The universal flip matrix and the generalized faro-shuffle. Pacific J. Math. 58 (1975), 445–455.
-
(1975)
Pacific J. Math.
, vol.58
, pp. 445-455
-
-
Hartwig, R.E.1
Morris, S.B.2
-
21
-
-
84984281904
-
Vec and vech operators for matrices, with some users in Jacobians and multivariate statistics
-
H.V. Henderson and S.R. Searle, Vec and vech operators for matrices, with some users in Jacobians and multivariate statistics. Canad. J. Statist. 7 (1979), 65–81.
-
(1979)
Canad. J. Statist.
, vol.7
, pp. 65-81
-
-
Henderson, H.V.1
Searle, S.R.2
-
22
-
-
34250590406
-
Uber die Darstellung der Determinante eines Systems, welches aus Zwei Anderen componirt ist
-
K. Hensel, Uber die Darstellung der Determinante eines Systems, welches aus Zwei Anderen componirt ist. Acta Math. 14 (1891), 317–319.
-
(1891)
Acta Math.
, vol.14
, pp. 317-319
-
-
Hensel, K.1
-
24
-
-
0015990655
-
The matrix equation AX + XB = C
-
V. Kucera, The matrix equation AX + XB = C. SIAM J. Appl. Math. 26 (1974), 15–25.
-
(1974)
SIAM J. Appl. Math.
, vol.26
, pp. 15-25
-
-
Kucera, V.1
-
26
-
-
0000321992
-
Explicit solutions of linear matrix equations
-
P. Lancaster, Explicit solutions of linear matrix equations. SIAM Rev. 12 (1970), 544–566.
-
(1970)
SIAM Rev.
, vol.12
, pp. 544-566
-
-
Lancaster, P.1
-
27
-
-
27644593943
-
On singular pencils of Zehfuss, compound, and Schläflian matrices
-
W. Ledermann, On singular pencils of Zehfuss, compound, and Schläflian matrices. Proc. Roy. Soc. Edinburgh LVI (1936), 50-89.
-
(1936)
Proc. Roy. Soc. Edinburgh
, vol.LVI
, pp. 50-89
-
-
Ledermann, W.1
-
28
-
-
25344452816
-
Multivariate normal estimation with missing data
-
M.Sc. Thesis, Dept. of Math., McGill University, Montreal
-
M.A. Legault-Giguère, Multivariate normal estimation with missing data. M.Sc. Thesis, Dept. of Math., McGill University, Montreal (1974).
-
(1974)
-
-
Legault-Giguère, M.A.1
-
29
-
-
84947528371
-
Kombinatorik, Determinaten und Matrices
-
E. Pascal, Teubner
-
A. Loewy, Kombinatorik, Determinaten und Matrices. Repertorium der Höheren Mathematik 1 (1910), 43–167. E. Pascal, Teubner.
-
(1910)
Repertorium der Höheren Mathematik
, vol.1
, pp. 43-167
-
-
Loewy, A.1
-
31
-
-
0000387723
-
Matrix derivatives with an application to an adaptive linear decision problem
-
E.C. MacRae, Matrix derivatives with an application to an adaptive linear decision problem. Ann. Statist. 2 (1974), 337–346.
-
(1974)
Ann. Statist.
, vol.2
, pp. 337-346
-
-
MacRae, E.C.1
-
32
-
-
0000489758
-
The commutation matrix: Some properties and applications
-
J.R. Magnus and H. Neudecker, The commutation matrix: Some properties and applications. Ann. Statist. 7 (1979), 381–394.
-
(1979)
Ann. Statist.
, vol.7
, pp. 381-394
-
-
Magnus, J.R.1
Neudecker, H.2
-
33
-
-
34948871657
-
The McDonald-Swaminathan matrix calculus: Clarifications, extensions, and illustrations
-
R.P. McDonald, The McDonald-Swaminathan matrix calculus: Clarifications, extensions, and illustrations. General Systems 21 (1976), 87–94.
-
(1976)
General Systems
, vol.21
, pp. 87-94
-
-
McDonald, R.P.1
-
34
-
-
0002770650
-
A simple matrix calculus with applications to multivariate analysis
-
R.P. McDonald and H. Swaminathan, A simple matrix calculus with applications to multivariate analysis. General Systems 18 (1973), 37–54.
-
(1973)
General Systems
, vol.18
, pp. 37-54
-
-
McDonald, R.P.1
Swaminathan, H.2
-
35
-
-
9644293166
-
The matrix equation AXB + CXD = E
-
S.K. Mitra, The matrix equation AXB + CXD = E. SIAM J. Appl. Math. 32 (1977), 823–825.
-
(1977)
SIAM J. Appl. Math.
, vol.32
, pp. 823-825
-
-
Mitra, S.K.1
-
36
-
-
49549135374
-
The generalized faro shuffle
-
S.B. Morris and R.E. Hartwig, The generalized faro shuffle. Discrete Math. 15 (1976), 333–346.
-
(1976)
Discrete Math.
, vol.15
, pp. 333-346
-
-
Morris, S.B.1
Hartwig, R.E.2
-
38
-
-
84915153498
-
On the symmetric multivariate normal distribution and asymptotic expansion of a Wishart matrix
-
D.G. Nel, On the symmetric multivariate normal distribution and asymptotic expansion of a Wishart matrix. South African Statist. J. 12 (1978), 145–159.
-
(1978)
South African Statist. J.
, vol.12
, pp. 145-159
-
-
Nel, D.G.1
-
39
-
-
0011658817
-
The Kronecker matrix product and some of its applications in econometrics
-
H. Neudecker, The Kronecker matrix product and some of its applications in econometrics. Statistica Neerlandica 22 (1968), 69–81.
-
(1968)
Statistica Neerlandica
, vol.22
, pp. 69-81
-
-
Neudecker, H.1
-
40
-
-
0342518329
-
A note on Kronecker matrix products and matrix equation systems
-
H. Neudecker, A note on Kronecker matrix products and matrix equation systems. SIAM J. Appl. Math. 17 (1969), 603–606.
-
(1969)
SIAM J. Appl. Math.
, vol.17
, pp. 603-606
-
-
Neudecker, H.1
-
41
-
-
0039119455
-
Some theorems on matrix differentiation with special reference to Kronecker matrix products
-
H. Neudecker, Some theorems on matrix differentiation with special reference to Kronecker matrix products. J. Amer. Statist. Assoc. 64 (1969), 953–963.
-
(1969)
J. Amer. Statist. Assoc.
, vol.64
, pp. 953-963
-
-
Neudecker, H.1
-
42
-
-
1542326720
-
A note on the variance of a matrix
-
D.H. Nissen, A note on the variance of a matrix. Econometrica 36 (1968), 603–604.
-
(1968)
Econometrica
, vol.36
, pp. 603-604
-
-
Nissen, D.H.1
-
44
-
-
84947516125
-
On testing a multivariate linear hypothesis when the covariance matrix and its inverse have the same pattern
-
G.S. Rogers and D.L. Young, On testing a multivariate linear hypothesis when the covariance matrix and its inverse have the same pattern. J. Amer. Statist. Assoc. 73 (1978), 203–207.
-
(1978)
J. Amer. Statist. Assoc.
, vol.73
, pp. 203-207
-
-
Rogers, G.S.1
Young, D.L.2
-
45
-
-
84966240253
-
On direct product matrices
-
W.E. Roth, On direct product matrices. Bull. Amer. Math. Soc. 40 (1934), 461–468.
-
(1934)
Bull. Amer. Math. Soc.
, vol.40
, pp. 461-468
-
-
Roth, W.E.1
-
46
-
-
84934318215
-
On the condition that two Zehfuss matrices be equal
-
D.E. Rutherford, On the condition that two Zehfuss matrices be equal. Bull. Amer. Math. Soc. 39 (1933), 801–808.
-
(1933)
Bull. Amer. Math. Soc.
, vol.39
, pp. 801-808
-
-
Rutherford, D.E.1
-
47
-
-
0004219915
-
Matrix Algebra for the Biological Sciences
-
John Wiley and Sons, New York
-
S.R. Searle, Matrix Algebra for the Biological Sciences. John Wiley and Sons, New York (1966).
-
(1966)
-
-
Searle, S.R.1
-
48
-
-
84892339604
-
A univariate formulation of the multivariate linear model
-
Papers in honor of H.O. Hartley (Ed. H.A. David). Academic Press
-
S.R. Searle, A univariate formulation of the multivariate linear model. Contributions to Survey Sampling and Applied Statistics, Papers in honor of H.O. Hartley (Ed. H.A. David). Academic Press (1978), 181–189.
-
(1978)
Contributions to Survey Sampling and Applied Statistics
, pp. 181-189
-
-
Searle, S.R.1
-
49
-
-
0009940043
-
Notes on variance component estimation: A detailed account of maximum likelihood and kindred methodology
-
Paper No. BU-673-M in the Biometrics Unit Mimeo Series, Cornell University
-
S.R. Searle, Notes on variance component estimation: A detailed account of maximum likelihood and kindred methodology. Paper No. BU-673-M in the Biometrics Unit Mimeo Series, Cornell University (1979).
-
(1979)
-
-
Searle, S.R.1
-
50
-
-
84918654144
-
Some generalizations in matrix differentiation with applications in multivariate analysis
-
Ph.D. Thesis, University of Windsor, Canada, 209 pp
-
R.P. Singh, Some generalizations in matrix differentiation with applications in multivariate analysis. Ph.D. Thesis, University of Windsor, Canada (1972). 209 pp.
-
(1972)
-
-
Singh, R.P.1
-
51
-
-
0038525498
-
Analysis of parametric structures for variance matrices
-
Ph.D. Thesis, Dept. of Statistics, University of Adelaide, Australia, 188 pp
-
A.J. Swain, Analysis of parametric structures for variance matrices. Ph.D. Thesis, Dept. of Statistics, University of Adelaide, Australia (1975). 188 pp.
-
(1975)
-
-
Swain, A.J.1
-
52
-
-
0041110637
-
Sur la solution du cas le plus général des équations linéaires en quantités binaires, c'est-à-dire en quaternions ou en matrices du second ordre
-
J. Sylvester, Sur la solution du cas le plus général des équations linéaires en quantités binaires, c'est-à-dire en quaternions ou en matrices du second ordre. C.R. Acad. Sci. Paris. 99 (1884), 117–118.
-
(1884)
C.R. Acad. Sci. Paris
, vol.99
, pp. 117-118
-
-
Sylvester, J.1
-
53
-
-
3643114480
-
Sur la résolution générale de l'équation linéaire en matrices d'un ordre quelconque
-
J. Sylvester, Sur la résolution générale de l'équation linéaire en matrices d'un ordre quelconque. C.R. Acad. Sci. Paris. 99 (1884), 409–412.
-
(1884)
C.R. Acad. Sci. Paris
, vol.99
, pp. 409-412
-
-
Sylvester, J.1
-
54
-
-
3643114480
-
Sur la résolution générale de l'équation linéaire en matrices d'un ordre quelconque
-
J. Sylvester, Sur la résolution générale de l'équation linéaire en matrices d'un ordre quelconque. C.R. Acad. Sci. Paris. 99 (1884), 432–436.
-
(1884)
C.R. Acad. Sci. Paris
, vol.99
, pp. 432-436
-
-
Sylvester, J.1
-
55
-
-
3743065438
-
Multivariate maxima and minima with matrix derivatives
-
D.S. Tracy and P.S. Dwyer, Multivariate maxima and minima with matrix derivatives. J. Amer. Statist. Assoc. 64 (1969), 1576–1594.
-
(1969)
J. Amer. Statist. Assoc.
, vol.64
, pp. 1576-1594
-
-
Tracy, D.S.1
Dwyer, P.S.2
-
56
-
-
84995108059
-
A new matrix product and its applications in partitioned matrices
-
D.S. Tracy and R.P. Singh, A new matrix product and its applications in partitioned matrices. Statistica Neerlandica 26 (1972), 143–157.
-
(1972)
Statistica Neerlandica
, vol.26
, pp. 143-157
-
-
Tracy, D.S.1
Singh, R.P.2
-
57
-
-
84915193193
-
Some modifications of matrix differentiation for evaluating Jacobians of symmetric matrix transformations
-
Proceedings of a symposium in honor of Paul S. Dwyer (Ed. Derrick S. Tracy), University of Windsor, Ontario, Canada
-
D.S. Tracy and R.P. Singh, Some modifications of matrix differentiation for evaluating Jacobians of symmetric matrix transformations. Symmetric Functions in Statistics, Proceedings of a symposium in honor of Paul S. Dwyer (Ed. Derrick S. Tracy), University of Windsor, Ontario, Canada (1972), 203–224.
-
(1972)
Symmetric Functions in Statistics
, pp. 203-224
-
-
Tracy, D.S.1
Singh, R.P.2
-
58
-
-
0242556869
-
On an application of Kronecker product of matrices to statistical designs
-
Nanohar N. Vartak, On an application of Kronecker product of matrices to statistical designs. Ann. Math. Statist. 26 (1955), 420–438.
-
(1955)
Ann. Math. Statist.
, vol.26
, pp. 420-438
-
-
Vartak, N.N.1
-
59
-
-
0014764195
-
Derivative operations on matrices
-
W.J. Vetter, Derivative operations on matrices. IEEE Trans. Automat. Contr. 15 (1970), 241–244.
-
(1970)
IEEE Trans. Automat. Contr.
, vol.15
, pp. 241-244
-
-
Vetter, W.J.1
-
60
-
-
0000029550
-
Matrix calculus operations and Taylor expansions
-
W.J. Vetter, Matrix calculus operations and Taylor expansions. SIAM Rev. 15 (1973), 352–369.
-
(1973)
SIAM Rev.
, vol.15
, pp. 352-369
-
-
Vetter, W.J.1
-
61
-
-
0016496210
-
Linear structures and solutions of linear matrix equations
-
W.J. Vetter, Linear structures and solutions of linear matrix equations. Linear Algebra and Appl. 10 (1975), 181–188.
-
(1975)
Linear Algebra and Appl.
, vol.10
, pp. 181-188
-
-
Vetter, W.J.1
-
62
-
-
84939021535
-
Properties of high radix fast Fourier-Hadamard transforms. Applications of Walsh functions
-
Washington, D.C. (Ed. C.A. Bass)
-
J.E. Whelchel, Jr. and D.F. Guinn, Properties of high radix fast Fourier-Hadamard transforms. Applications of Walsh functions. 1970 Proceedings symposium and workshop held at Naval Research Laboratory, Washington, D.C. (Ed. C.A. Bass) (1970). 80–87.
-
(1970)
1970 Proceedings symposium and workshop held at Naval Research Laboratory
, pp. 80-87
-
-
Whelchel, J.E.1
Guinn, D.F.2
-
63
-
-
60949105558
-
Ueber eine gewisje Determinante
-
G. Zehfuss, Ueber eine gewisje Determinante. Z. Math. Phys. 3 (1858), 298–301.
-
(1858)
Z. Math. Phys.
, vol.3
, pp. 298-301
-
-
Zehfuss, G.1
|