The Largest Eigenvalue of a Positive Definite Symmetric Matrix: 10839

2002 ◽  
Vol 109 (10) ◽  
pp. 922
Author(s):  
Beresford N. Parlett ◽  
Olaf Krafft ◽  
Martin Schaefer
Keyword(s):  
Symmetric Matrix ◽  
Positive Definite ◽  
Largest Eigenvalue ◽  
Positive Definite Symmetric Matrix ◽  
Definite Symmetric Matrix ◽  
The Largest Eigenvalue

Decomposition of the Multivariate Beta Distribution with Applications

1972 ◽  
Vol 15 (2) ◽  
pp. 225-228 ◽  
Author(s):  
D. G. Kabe ◽  
R. P. Gupta
Keyword(s):  
Beta Distribution ◽  
Symmetric Matrix ◽  
Positive Definite ◽  
Arbitrary Rank ◽  
Positive Definite Symmetric Matrix ◽  
Multivariate Beta ◽  
Explicit Procedure ◽  
Definite Symmetric Matrix ◽  
Multivariate Beta Distribution

SummaryLet L be a positive definite symmetric matrix having a noncentral multivariate beta density of an arbitrary rank, see, e.g. Hayakawa ([2, p. 12, Equation 38]). Then an explicit procedure is given for decomposing the density of L in terms of densities of independent beta variates.

MATRIX STUDY OF THE EQUATION OF SOLID RIGID MOTIONS

2021 ◽  
Vol 10 (9) ◽  
pp. 3195-3207
Author(s):  
K. Atchonouglo ◽  
K. Nwuitcha
Keyword(s):  
Symmetric Matrix ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Positive Definite ◽  
Matrix Formulation ◽  
Total Body Mass ◽  
Positive Definite Symmetric Matrix ◽  
Rigid Motions ◽  
Definite Symmetric Matrix ◽  
Total Body

In this article, we described the equations of motion of a rigid solid by a matrix formulation. The matrices contained in our movement description are homogeneous to the same unit. Inertial characteristics are met in a 4x4 positive definite symmetric matrix called "tensor generalized Poinsot." This matrix consists of 3x3 positive definite symmetric matrix called "inertia tensor Poinsot", the coordinates of the center of mass multiplied by the total body mass and the total mass of the rigid body. The equations of motion are formulated as a gender skew 4x4 matrices. They summarize the "principle of fundamental dynamics". The Poinsot generalized tensor appears linearly in this equality as required by the linear dependence of the equations of motion with the ten characteristics inertia of the rigid solid.

scholarly journals G2-metrics arising from non-integrable special Lagrangian fibrations

2019 ◽  
Vol 6 (1) ◽  
pp. 348-365 ◽  
Author(s):  
Ryohei Chihara
Keyword(s):  
Dynamical Systems ◽  
Symmetric Matrix ◽  
Positive Definite ◽  
Special Lagrangian ◽  
3 Dimensional ◽  
Dimensional Group ◽  
Constrained Dynamical Systems ◽  
Definite Symmetric Matrix ◽  
Type 3 ◽  
Torsion Free

AbstractWe study special Lagrangian fibrations of SU(3)-manifolds, not necessarily torsion-free. In the case where the fiber is a unimodular Lie group G, we decompose such SU(3)-structures into triples of solder 1-forms, connection 1-forms and equivariant 3 × 3 positive-definite symmetric matrix-valued functions on principal G-bundles over 3-manifolds. As applications, we describe regular parts of G2-manifolds that admit Lagrangian-type 3-dimensional group actions by constrained dynamical systems on the spaces of the triples in the cases of G = T3 and SO(3).

Estimating the Largest Eigenvalue of a Positive Definite Matrix

1979 ◽  
Vol 33 (148) ◽  
pp. 1289 ◽  
Author(s):  
Dianne P. O'Leary ◽  
G. W. Stewart ◽  
James S. Vandergraft
Keyword(s):  
Positive Definite Matrix ◽  
Positive Definite ◽  
Largest Eigenvalue ◽  
The Largest Eigenvalue
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