scholarly journals Trace of Positive Integer Power of Squared Special Matrix

CAUCHY ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 200-211
Author(s):  
Rahmawati Rahmawati ◽  
Aryati Citra ◽  
Fitri Aryani ◽  
Corry Corazon Marzuki ◽  
Yuslenita Muda
Keyword(s):  
Positive Integer ◽  
Direct Proof ◽  
Integer Power ◽  
The Matrix ◽  
Special Matrix ◽  
Matrix Trace

The rectangle matrix to be discussed in this research is a special matrix where each entry in each line has the same value which is notated by An. The main aim of this paper is to find the general form of the matrix trace An powered positive integer m. To prove whether the general form of the matrix trace of An powered positive integer can be confirmed, mathematics induction and direct proof are used.  

Trace Matriks Berbentuk Khusus 2 X 2 Berpangkat Bilangan Bulat Positif

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Fitri Aryani ◽  
Titik Fatonah
Keyword(s):  
Positive Integer ◽  
Direct Proof ◽  
Mathematical Induction ◽  
Main Diagonal ◽  
General Shape ◽  
Integer Power ◽  
Square Matrix

Trace matriks ialah jumlah dari elemen diagonal utama dari matriks kuadrat. Penelitian ini membahas mengenai jejak kekuatan bilangan bulat positif matriks nyata 2x2. Ada dua langkah dalam membentuk bentuk umum dari trace matriks. Pertama, tentukan bentuk umum (An) dan buktikan menggunakan induksi matematika. Kedua, tentukan jejak bentuk umum (An) dan buktikan dengan bukti langsung. Hasilnya diperoleh bentuk umum jejak daya bilangan bulat positif dari matriks nyata 2x2 nyata untuk n ganjil dan n genap.   Trace matrix is ​​the sum of the main diagonal elements of the square matrix. This Paper discusses the trace of positive integer power of  real 2x2 special matrices. There are two steps in forming the general shape of the trace matrix. First, determine the general form of (An) and prove it using mathematical induction. Second, determine the general form trace (An) and prove it by direct proof. The results obtained a general shape of trace of positive integer power power of  real 2x2 special matrices for n odd and n even.

scholarly journals On normal numbers

1982 ◽  
Vol 32 (1) ◽  
pp. 79-87 ◽  
Author(s):  
C. E. M. Pearce ◽  
M. S. Keane
Keyword(s):  
Positive Integer ◽  
Simple Proof ◽  
Normal Numbers ◽  
Integer Power ◽  
Positive Integers

AbstractSchmidt has shown that if r and s are positive integers and there is no positive integer power of r which is also a positive integer power of s, then there exists an uncountable set of reals which are normal to base r but not even simply normal to base s. We give a structurally simple proof of this result

scholarly journals The normalizer of Γ0(N) in PSL(2, ℝ)

1990 ◽  
Vol 32 (3) ◽  
pp. 317-327 ◽  
Author(s):  
M. Akbas ◽  
D. Singerman
Keyword(s):  
Positive Integer ◽  
Modular Group ◽  
Prime Divisors ◽  
Möbius Transformations ◽  
The Matrix ◽  
Image Position ◽  
Mobius Transformations

Let Γ denote the modular group, consisting of the Möbius transformationsAs usual we denote the above transformation by the matrix remembering that V and – V represent the same transformation. If N is a positive integer we let Γ0(N) denote the transformations for which c ≡ 0 mod N. Then Γ0(N) is a subgroup of indexthe product being taken over all prime divisors of N.

scholarly journals MATRIX TRACE INEQUALITIES RELATED TO UNCERTAINTY PRINCIPLE

2005 ◽  
Vol 16 (06) ◽  
pp. 629-645 ◽  
Author(s):  
HIDEKI KOSAKI
Keyword(s):  
Uncertainty Principle ◽  
Recent Article ◽  
Trace Inequality ◽  
The Matrix ◽  
Trace Inequalities ◽  
Matrix Trace

In their recent article, Luo and Zhang conjectured the matrix trace inequality mentioned in the introduction below, which is motivated by uncertainty principle. We present a proof for the conjectured inequality.

scholarly journals Geometric Construction of Some Lehmer Means

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 251 ◽  
Author(s):  
Ralph Høibakk ◽  
Dag Lukkassen ◽  
Annette Meidell ◽  
Lars-Erik Persson
Keyword(s):  
Positive Integer ◽  
Geometric Construction ◽  
Geometric Constructions ◽  
Line Segments ◽  
Integer Power

The main aim of this paper is to contribute to the recently initiated research concerning geometric constructions of means, where the variables are appearing as line segments. The present study shows that all Lehmer means of two variables for integer power k and for k = m 2 , where m is an integer, can be geometrically constructed, that Lehmer means for power k = 0 , 1 and 2 can be geometrically constructed for any number of variables and that Lehmer means for power k = 1 / 2 and - 1 can be geometrically constructed, where the number of variables is n = 2 m and m is a positive integer.

Computation of Fourier transform representations involving the generalized Bessel matrix polynomials

2021 ◽  
Author(s):  
mohamed abdalla
Keyword(s):  
Fourier Transform ◽  
Orthogonal Polynomials ◽  
Integral Transforms ◽  
General Character ◽  
Matrix Functions ◽  
Fourier Cosine ◽  
Matrix Polynomials ◽  
The Matrix ◽  
Special Matrix ◽  
Special Matrix Functions

Abstract Motivated by the recent studies and developments of the integral transforms with various special matrix functions, including the matrix orthogonal polynomials as kernels. In this article, we derive the formulas for Fourier cosine transforms and Fourier sine transforms of matrix functions involving generalized Bessel matrix polynomials. With the help of these transforms a number of results are considered which are extensions of the corresponding results in the standard cases. The results given here are of general character and can yield a number of (known and new) results in modern integral transforms.

scholarly journals Convex Coupled Matrix and Tensor Completion

2018 ◽  
Vol 30 (11) ◽  
pp. 3095-3127 ◽  
Author(s):  
Kishan Wimalawarne ◽  
Makoto Yamada ◽  
Hiroshi Mamitsuka
Keyword(s):  
Optimal Solution ◽  
Real Data ◽  
Excess Risk ◽  
Low Rank ◽  
Trace Norm ◽  
Tensor Completion ◽  
The Matrix ◽  
Risk Bounds ◽  
Matrix Trace

We propose a set of convex low-rank inducing norms for coupled matrices and tensors (hereafter referred to as coupled tensors), in which information is shared between the matrices and tensors through common modes. More specifically, we first propose a mixture of the overlapped trace norm and the latent norms with the matrix trace norm, and then, propose a completion model regularized using these norms to impute coupled tensors. A key advantage of the proposed norms is that they are convex and can be used to find a globally optimal solution, whereas existing methods for coupled learning are nonconvex. We also analyze the excess risk bounds of the completion model regularized using our proposed norms and show that they can exploit the low-rankness of coupled tensors, leading to better bounds compared to those obtained using uncoupled norms. Through synthetic and real-data experiments, we show that the proposed completion model compares favorably with existing ones.

scholarly journals The Adjacency Matrix of One Type of Directed Graph and the Jacobsthal Numbers and Their Determinantal Representation

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Fatih Yılmaz ◽  
Durmuş Bozkurt
Keyword(s):  
Graph Theory ◽  
Positive Integer ◽  
Directed Graph ◽  
Adjacency Matrix ◽  
Intensive Study ◽  
Integer Power ◽  
Determinantal Representation ◽  
Adjacency Matrices

Recently there is huge interest in graph theory and intensive study on computing integer powers of matrices. In this paper, we consider one type of directed graph. Then we obtain a general form of the adjacency matrices of the graph. By using the well-known property which states the(i,j)entry ofAm(Ais adjacency matrix) is equal to the number of walks of lengthmfrom vertexito vertexj, we show that elements ofmth positive integer power of the adjacency matrix correspond to well-known Jacobsthal numbers. As a consequence, we give a Cassini-like formula for Jacobsthal numbers. We also give a matrix whose permanents are Jacobsthal numbers.

NTH‐ROOT STACK NONLINEAR MULTICHANNEL FILTER

Geophysics ◽  
1973 ◽  
Vol 38 (2) ◽  
pp. 327-338 ◽  
Author(s):  
E. R. Kanasewich ◽  
C. D. Hemmings ◽  
T. Alpaslan
Keyword(s):  
Positive Integer ◽  
Phase Velocity ◽  
Random Noise ◽  
Seismic Refraction ◽  
Nonlinear Filter ◽  
Linear Filter ◽  
Data Set ◽  
Multichannel Filter ◽  
The Matrix ◽  
Actual Field

A nonlinear multichannel filter is developed which appears to be particularly useful for enhancement of seismic refraction and teleseismic array data. The basic filter involves the extraction of the Nth root of each element in the matrix forming the data set, where N is any positive integer, and the Nth power of the summation over the channels. The filter is effective in reducing random noise, whereas identical signals which are in‐phase on all channels are retained at the expense of some distortion. The output from this nonlinear filter has far greater resolution in specifying phase velocity than any multichannel linear filter we have employed. Examples of theoretical and actual field seismograms are presented after various forms of filtering to illustrate their effectiveness.

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