Details
| Original language | English |
|---|---|
| Article number | 168 |
| Number of pages | 16 |
| Journal | Journal of Inequalities and Applications |
| Volume | 2013 |
| Publication status | Published - 12 Apr 2013 |
| Externally published | Yes |
Abstract
Let [InlineEquation not available: see fulltext.] be such that [InlineEquation not available: see fulltext.] and [Equation not available: see fulltext.] Then [Equation not available: see fulltext.] This can also be stated in terms of real positive definite [InlineEquation not available: see fulltext.]-matrices [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.]: If their determinants are equal, [InlineEquation not available: see fulltext.], then [Equation not available: see fulltext.] where log is the principal matrix logarithm and [InlineEquation not available: see fulltext.] denotes the Frobenius matrix norm. Applications in matrix analysis and nonlinear elasticity are indicated. MSC: 26D05, 26D07.
Keywords
- characteristic polynomial, elementary symmetric polynomials, inequality, matrix logarithm, means, positive definite matrices
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Discrete Mathematics and Combinatorics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Inequalities and Applications, Vol. 2013, 168, 12.04.2013.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Sum of squared logarithms
T2 - an inequality relating positive definite matrices and their matrix logarithm
AU - Bîrsan, Mircea
AU - Neff, Patrizio
AU - Lankeit, Johannes
N1 - Funding Information: The first author (MB) was supported by the German state grant: ‘Programm des Bundes und der Länder für bessere Studienbedingungen und mehr Qualität in der Lehre’.
PY - 2013/4/12
Y1 - 2013/4/12
N2 - Let [InlineEquation not available: see fulltext.] be such that [InlineEquation not available: see fulltext.] and [Equation not available: see fulltext.] Then [Equation not available: see fulltext.] This can also be stated in terms of real positive definite [InlineEquation not available: see fulltext.]-matrices [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.]: If their determinants are equal, [InlineEquation not available: see fulltext.], then [Equation not available: see fulltext.] where log is the principal matrix logarithm and [InlineEquation not available: see fulltext.] denotes the Frobenius matrix norm. Applications in matrix analysis and nonlinear elasticity are indicated. MSC: 26D05, 26D07.
AB - Let [InlineEquation not available: see fulltext.] be such that [InlineEquation not available: see fulltext.] and [Equation not available: see fulltext.] Then [Equation not available: see fulltext.] This can also be stated in terms of real positive definite [InlineEquation not available: see fulltext.]-matrices [InlineEquation not available: see fulltext.], [InlineEquation not available: see fulltext.]: If their determinants are equal, [InlineEquation not available: see fulltext.], then [Equation not available: see fulltext.] where log is the principal matrix logarithm and [InlineEquation not available: see fulltext.] denotes the Frobenius matrix norm. Applications in matrix analysis and nonlinear elasticity are indicated. MSC: 26D05, 26D07.
KW - characteristic polynomial
KW - elementary symmetric polynomials
KW - inequality
KW - matrix logarithm
KW - means
KW - positive definite matrices
UR - http://www.scopus.com/inward/record.url?scp=84879893147&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1301.6604
DO - 10.48550/arXiv.1301.6604
M3 - Article
AN - SCOPUS:84879893147
VL - 2013
JO - Journal of Inequalities and Applications
JF - Journal of Inequalities and Applications
SN - 1025-5834
M1 - 168
ER -