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 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.  

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 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.

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.

scholarly journals Trace of Positive Integer Power of Real 2 × 2 Matrices

2015 ◽  
Vol 05 (04) ◽  
pp. 150-155 ◽  
Author(s):  
Jagdish Pahade ◽  
Manoj Jha
Keyword(s):  
Positive Integer ◽  
Integer Power

On C-Matrices of Arbitrary Powers

1971 ◽  
Vol 23 (3) ◽  
pp. 531-535 ◽  
Author(s):  
Richard J. Turyn
Keyword(s):  
Finite Field ◽  
Prime Power ◽  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Main Diagonal ◽  
Quadratic Character ◽  
Symmetric Complex ◽  
Complex Hadamard Matrix ◽  
Square Matrix

A C-matrix is a square matrix of order m + 1 which is 0 on the main diagonal, has ±1 entries elsewhere and satisfies . Thus, if , I + C is an Hadamard matrix of skew type [3; 6] and, if , iI + C is a (symmetric) complex Hadamard matrix [4]. For m > 1, we must have . Such matrices arise from the quadratic character χ in a finite field, when m is an odd prime power, as [χ(ai – aj)] suitably bordered, and also from some other constructions, in particular those of skew type Hadamard matrices. (For we must have m = a2 + b2, a, b integers.)

scholarly journals ANALISIS KEMAMPUAN PENALARAN MATEMATIK SISWA SMP PADA SOAL-SOAL MATERI SEGI EMPAT DAN SEGITIGA

2018 ◽  
Vol 1 (4) ◽  
pp. 807
Author(s):  
Puji Astuti ◽  
Ratna Sariningsih
Keyword(s):  
Junior High School ◽  
Research Method ◽  
Mathematical Reasoning ◽  
Direct Proof ◽  
Mathematical Induction ◽  
Reasoning Ability ◽  
Research Subjects ◽  
Relationship Patterns ◽  
Solution Processes ◽  
Class Viii

This research aims to determine the ability of mathematical reasoning of students of class VIII SMP about the rectangular and triangular material. The research method used is descriptive qualitative research. Subjects in this study were 30 students in one junior high school in Cianjur District. The reasoning ability reasoning instrument used is an essay form. Indicator used in this research there are 7 indicators of reasoning ability that is drawing logical conclusion; provide explanations using images; establishing direct proof, indirect proof, and by proving by mathematical induction; filed the infringement rules, checked the validity of the arguments and compiled a valid argument; propose opponent example; estimate answers and solution processes; using relationship patterns to analyze, make analogies, generalizations, and compile and test conjectures.

scholarly journals Infinite product expansions for matrix n-th roots

1968 ◽  
Vol 8 (2) ◽  
pp. 242-249 ◽  
Author(s):  
R. A. Smith
Keyword(s):  
Positive Integer ◽  
Banach Algebra ◽  
Spectral Radius ◽  
Iterative Procedure ◽  
Infinite Product ◽  
Matrix Norm ◽  
Binomial Series ◽  
Image Position ◽  
Square Matrix

In this paper a denotes a square matrix with real or complex elements (though the theorems and their proofs are valid in any Banach algebra). Its spectral radius p(a) is given by with any matrix norm (see [4], p. 183). If p(a) < 1 and n is a positive integer then the binomial series converges and its sum satisfies S(a)n = (1−a)−1. Let where q is any integer exceeding 1. Then u(a) is the sum of the first q terms of the series (2). Write and let a0, a1, a2,…be the sequence of matrices obtained by the iterative procedure Defining polynomials φ0(x), φ1(x), φ2(x),…inductively by we have aν = φν (a) and therefore aμaν = aνaμ for all 4 μ, ν. The following is proved in section 2: Theorem 1. If ρ(a) < 1 thenconverges and P(a) = S(a). Furthermore, if p(a) < r < 1, thenfor all ν, where M depends on r and a but is independent of ν and q.

scholarly journals One Can Hear the Area of a Torus by Hearing the Eigenvalues of the Polyharmonic Operators

2014 ◽  
Vol 47 (3) ◽  
Author(s):  
Shunzi Guo ◽  
Jinyun Jin
Keyword(s):  
Positive Integer ◽  
Asymptotic Formula ◽  
Spectral Problem ◽  
Asymptotic Properties ◽  
Beltrami Operator ◽  
Dimensional Torus ◽  
Integer Power ◽  
Real Positive Number

AbstractThis paper considers the asymptotic properties for the spectrum of a positive integer power l of the Laplace-Beltrami operator acting on an n-dimensional torus T. If N(λ) is the number of eigenvalues counted with multiplicity, smaller than a real positive number, we establish a Weyl-type asymptotic formula for the spectral problem of the polyharmonic operators on T, that is, as λ → +∞N (λ) ~ ωwhere ω

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