An Idempotent Matrix

1962 ◽  
Vol 35 (1) ◽  
pp. 53-54
Author(s):  
J. L. Stearn
Keyword(s):  
Idempotent Matrix

The Modified Power Method for Solving the Eigenvalue Problem with the Use of Idempotent Matrix

2015 ◽  
Vol 712 ◽  
pp. 43-48
Author(s):  
Rafał Palej ◽  
Artur Krowiak ◽  
Renata Filipowska
Keyword(s):  
Eigenvalue Problem ◽  
Rate Of Convergence ◽  
Rayleigh Quotient ◽  
Frobenius Norm ◽  
Dominant Eigenvalue ◽  
Power Method ◽  
New Approach ◽  
Idempotent Matrix ◽  
The Given ◽  
Scaling Coefficient

The work presents a new approach to the power method serving the purpose of solving the eigenvalue problem of a matrix. Instead of calculating the eigenvector corresponding to the dominant eigenvalue from the formula , the idempotent matrix B associated with the given matrix A is calculated from the formula , where m stands for the method’s rate of convergence. The scaling coefficient ki is determined by the quotient of any norms of matrices Bi and or by the reciprocal of the Frobenius norm of matrix Bi. In the presented approach the condition for completing calculations has the form. Once the calculations are completed, the columns of matrix B are vectors parallel to the eigenvector corresponding to the dominant eigenvalue, which is calculated from the Rayleigh quotient. The new approach eliminates the necessity to use a starting vector, increases the rate of convergence and shortens the calculation time when compared to the classic method.

Linear dynamical systems of dimension two over the ring of integers modulo pt

2020 ◽  
Vol 12 (06) ◽  
pp. 2050074
Author(s):  
Yangjiang Wei ◽  
Heyan Xu ◽  
Linhua Liang
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Diagonal Matrix ◽  
Linear Dynamical System ◽  
Linear Dynamical Systems ◽  
Ring Of Integers ◽  
Idempotent Matrix ◽  
Nilpotent Matrix ◽  
Matrix Formula

In this paper, we investigate the linear dynamical system [Formula: see text], where [Formula: see text] is the ring of integers modulo [Formula: see text] ([Formula: see text] is a prime). In order to facilitate the visualization of this system, we associate a graph [Formula: see text] on it, whose nodes are the points of [Formula: see text], and for which there is an arrow from [Formula: see text] to [Formula: see text], when [Formula: see text] for a fixed [Formula: see text] matrix [Formula: see text]. In this paper, the in-degree of each node in [Formula: see text] is obtained, and a complete description of [Formula: see text] is given, when [Formula: see text] is an idempotent matrix, or a nilpotent matrix, or a diagonal matrix. The results in this paper generalize Elspas’ [1959] and Toledo’s [2005].

scholarly journals The Tropical Matrix Groups with Symmetric Idempotents

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Lin Yang
Keyword(s):  
Diagonal Matrix ◽  
Main Diagonal ◽  
Diagonal Block ◽  
Maximal Subgroups ◽  
Block Diagonal Matrix ◽  
Matrix Groups ◽  
Idempotent Matrix ◽  
Block Idempotent ◽  
Real Matrices ◽  
Block Diagonal

In this paper we study the semigroup Mn(T) of all n×n tropical matrices under multiplication. We give a description of the tropical matrix groups containing a diagonal block idempotent matrix in which the main diagonal blocks are real matrices and other blocks are zero matrices. We show that each nonsingular symmetric idempotent matrix is equivalent to this type of block diagonal matrix. Based upon this result, we give some decompositions of the maximal subgroups of Mn(T) which contain symmetric idempotents.

scholarly journals Idempotency of linear combinations of an idempotent matrix and a tripotent matrix

2002 ◽  
Vol 354 (1-3) ◽  
pp. 21-34 ◽  
Author(s):  
Jerzy K. Baksalary ◽  
Oskar Maria Baksalary ◽  
George P.H. Styan
Keyword(s):  
Linear Combinations ◽  
Idempotent Matrix

Properties of Idempotent Matrix

1997 ◽  
Vol 13 (4) ◽  
pp. 606-606 ◽  
Author(s):  
Robert E. Hartwig ◽  
Götz Trenkler
Keyword(s):  
Idempotent Matrix
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