A dominance theorem for partitioned Hermitian matrices

Author:
Russell Merris

Journal:
Trans. Amer. Math. Soc. **164** (1972), 341-352

MSC:
Primary 15A48

DOI:
https://doi.org/10.1090/S0002-9947-1972-0296091-9

MathSciNet review:
0296091

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a partitioned positive semidefinite hermitian matrix, where is *n*-square, . A class of ordered pairs of functions is given such that is positive semidefinite hermitian. Applications are given.

**[1]**J. de Pillis,*Transformations on partitioned matrices*, Duke Math. J.**36**(1969), 511–515. MR**0325649****[2]**Walter Feit,*Characters of finite groups*, W. A. Benjamin, Inc., New York-Amsterdam, 1967. MR**0219636****[3]**Ralph Freese,*Inequalities for generalized matrix functions based on arbitrary characters*, Linear Algebra and Appl.**7**(1973), 337–345. MR**0340273****[4]**Paul R. Halmos,*Finite-dimensional vector spaces*, The University Series in Undergraduate Mathematics, D. Van Nostrand Co., Inc., Princeton-Toronto-New York-London, 1958. 2nd ed. MR**0089819****[5]**Charles Löwner,*Some theorems on positive matrices*(unpublished).**[6]**Marvin Marcus and Susan M. Katz,*Matrices of Schur functions*, Duke Math. J.**36**(1969), 343–352. MR**0242855****[7]**M. Marcus and N. A. Khan,*A note on the Hadamard product*, Canad. Math. Bull.**2**(1959), 81–83. MR**0105424**, https://doi.org/10.4153/CMB-1959-012-2**[8]**Marvin Marcus and Henryk Minc,*Generalized matrix functions*, Trans. Amer. Math. Soc.**116**(1965), 316–329. MR**0194445**, https://doi.org/10.1090/S0002-9947-1965-0194445-9**[9]**Marvin Marcus and Paul J. Nikolai,*Inequalities for some monotone matrix functions*, Canad. J. Math.**21**(1969), 485–494. MR**0237534**, https://doi.org/10.4153/CJM-1969-054-5**[10]**Marvin Marcus and William Watkins,*Partitioned hermitian matrices*, Duke Math. J.**38**(1971), 237–249. MR**0274479****[11]**Russell Merris,*Trace functions. I*, Duke Math. J.**38**(1971), 527–530. MR**0280506****[12]**Russell Merris,*Partitioned hermitian matrices*, J. Res. Nat. Bur. Standards Sect. B**74B**(1970), 45–46. MR**0266946****[13]**Russell Merris and William Watkins,*Group algebra ideals and symmetry classes of tensors*(to appear).**[14]**Morris Newman,*Matrix representations of groups*, National Bureau of Standards Applied Mathematics Series, vol. 60, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1968. MR**0246981****[15]**I. Schur,*Über endliche Gruppen und Hermitesche Formen*, Math. Z.**1**(1918), no. 2-3, 184–207 (German). MR**1544291**, https://doi.org/10.1007/BF01203611**[16]**S. G. Williamson,*On a class of combinatorial inequalities*, J. Combinatorial Theory**6**(1969), 359–369. MR**0238873**

Retrieve articles in *Transactions of the American Mathematical Society*
with MSC:
15A48

Retrieve articles in all journals with MSC: 15A48

Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1972-0296091-9

Keywords:
Generalized matrix function,
Schur function,
associated transformation,
Kronecker product,
Hadamard (Schur) product,
(group) character,
orthogonality relations

Article copyright:
© Copyright 1972
American Mathematical Society