Learning the concept of eigenvalues and eigenvectors: a comparative analysis of achieved concept construction in linear algebra using APOS theory among students from different educational backgrounds

ZDM ◽  
2019 ◽  
Vol 51 (7) ◽  
pp. 1125-1140 ◽  
Author(s):  
Mike Altieri ◽  
Evelyn Schirmer
Keyword(s):  
Comparative Analysis ◽  
Linear Algebra ◽  
Eigenvalues And Eigenvectors ◽  
Apos Theory ◽  
Educational Backgrounds

Vectors and Functions and Operators

2020 ◽  
pp. 3-13
Author(s):  
Jochen Autschbach
Keyword(s):  
Linear Algebra ◽  
Scalar Product ◽  
Cross Product ◽  
Eigenvalues And Eigenvectors ◽  
Laplace Operators

This chapter introduces – briefly – vectors and functions and the similarities between them, some basic linear algebra concepts, operators (including the del and Laplace operators), eigenvalues and eigenvectors &eigenfunctions, the scalar (dot) and vector (cross) product between two vectors, the scalar product between two functions, the concepts of normalization, orthogonality, and orthonormality. The concept of an operator is first introduced by considering the rotation and stretching or compression of a vector. It is then generalized to a mathematical prescription that changes a function into another function.

scholarly journals Autovalores e autovetores: utilização na classificação de relevância

2019 ◽  
Vol 40 ◽  
pp. 255
Author(s):  
Mylena Roehrs ◽  
Larissa Melchiors Furlan ◽  
Glauber Rodrigues de Quadros
Keyword(s):  
Markov Chains ◽  
Mathematical Models ◽  
Linear Algebra ◽  
Eigenvalues And Eigenvectors

The use of eigenvalues and eigenvectors, topic studied in Linear Algebra, extends to several other areas, such as engineering, genetics, geography, economics, etc. In all these areas there are many applications. The main objective of this work is to study and develop some of these applications of eigenvalues and eigenvectors in solving problems. Methods of ranking are presented using these concepts and presenting hypothetical situations as examples. In addition, mathematical models are constructed using Markov Chains. 

Business Process Models Representation by Deducing Interpretative Evidences on Intuitively Common Symbols

2012 ◽  
Vol 1 (1) ◽  
pp. 29-39
Author(s):  
Saleh Alwahaishi ◽  
Ahmad Jaffar ◽  
Ivo Vondrák ◽  
Václav Snášel
Keyword(s):  
Comparative Analysis ◽  
Business Process ◽  
Business Processes ◽  
Process Models ◽  
Reasonable Doubt ◽  
Significant Preference ◽  
Business Process Models ◽  
Educational Backgrounds ◽  
Interpretative Analysis ◽  
Modeling Techniques

Through quantitative analysis, previous researchers have proven a significant preference towards a specific set of notations for modeling business processes. The drawn conclusion revealed a significantly correlated coefficient preference to Norm Process Chart for using easily recognizable symbols to intuitively elicit understanding in representing business process models. Further interpretative analysis to qualitatively enhance these findings will only prove and strengthen the above claimed beyond reasonable doubt. The approach is to measure respondent level of accuracy in interpreting 3 different case studies modeled using 3 different modeling techniques shown to respondents in 3 different randomized sequences. The analysis includes correlating the finding against the time taken as well as respondents’ level of confidence in interpreting these models. The significantly correlated results again confirmed beyond reasonable doubt Norm Process Chart being respondents ultimate choice. Further comparative analysis between results from an earlier investigation against the latter, revealed similar patterns in respondents’ responses despite respondents dispersed ethnicity and educational backgrounds.

scholarly journals Spectrum Matriks Detour dari Graf Roda dengan n +1 Titik W_n

2020 ◽  
Vol 3 (1) ◽  
pp. 32
Author(s):  
Muhammad Abdy ◽  
Rahmat Syam ◽  
Agnes Monica Putri
Keyword(s):  
Graph Theory ◽  
Linear Algebra ◽  
Eigenvalues And Eigenvectors ◽  
Interesting Topic ◽  
Order Matrix ◽  
Wheel Graph

Penelitian ini bertujuan untuk  menentukan spectrum matriks detour dari graf roda dengan n+1 titik Wn. Spectrum dalam teori graf merupakan suatu topik menarik untuk dikaji dengan mempertemukan teori graf dan aljabar linear. Bentuk spectrum matriks detour adalah salah satu spectrum yang dapat ditentukan dalam graf roda. Matriks berordo (2 × n) yang terdiri dari nilai eigen berbeda dan banyak basis ruang eigen dari matriks terhubung langsung graf roda merupakan spectrum dari graf roda. Hasil penelitian ini menunjukkan bahwa langkah-langkah dalam menentukan spectrum matriks detour dari graf roda n+1 titik Wn, yaitu: menentukan graf roda dengan n + 1 titik Wn; menentukan detour, nilai eigen dan vektor eigen dari graf roda dengan n + 1 titik Wn,; melihat spectrum dan pola spectrum matriks detour dari graf roda n+1 titik Wn; pola yang didapat berupa dugaan kemudian dibuktikan dengan merumuskan suatu teorema yang dilengkapi dengan bukti.   Kata Kunci: Spectrum, Matriks Detour, Graf RodaThis study aims to determine the spectrum of detour matrix from the wheel graph with n+1 point Wn. Spectrum in graph theory is an interesting topic to review by bringing together graph theory and linear algebra. The form of the spectrum of detour matrix is one of the spectrums that can be determined in the wheel graph. The order matrix (2 × n) which consists of different eigenvalues and many the eigen space base from matrix adjacent wheel graph  is the spectrum of wheel graph. The results of this study show that steps in determining spectrum of detour matrix from the wheel graph with n+1 point Wn, that is: determine the wheel graph with n+1 point Wn; determine the detour; eigenvalues and eigenvectors of the wheel graph with n+1 point Wn; see the spectrum and patterns spectrum of detour matrix from the wheel graph with n+1 point Wn; pattern obtained in the form of conjecture then proved by formulating a theorem equipped with proof.Keywords: Spectrum, Detour Matrix, Wheel Graph.

scholarly journals Does The Use of APOS Theory Promote Students’ Achievement in Elementary Linear Algebra?

2021 ◽  
Vol 14 (3) ◽  
pp. 175-186
Author(s):  
I Made Arnawa ◽  
◽  
Yanita Yanita ◽  
Yerizon Yerizon ◽  
Bukti Ginting ◽  
...  
Keyword(s):  
Linear Algebra ◽  
Apos Theory

scholarly journals The Impact of the Modern Egyptian City on Egyptian Contemporary Painting: A Comparative Analysis of Five Contemporary Egyptian Models

2017 ◽  
Vol 1 (1) ◽  
pp. 6
Author(s):  
Marwa Mohammed Shazly
Keyword(s):  
Comparative Analysis ◽  
Educational Backgrounds ◽  
The People ◽  
The Future ◽  
Different Ages ◽  
Contemporary Painting ◽  
The Impact

The view of the outside scene of one of the cities in the painting is an expression mainly used about history and identity. It also expresses the last imagination and prophecy of the future. Not Just an embodiment of the scene in the street or part of a building or a temple in the picture, but it is a reflection of the identity of the people in all its elements.The search is a selective study of a group of contemporary Egyptian artists who dealt with the theme "landscape" of contemporary photography in Egypt is: Fathi Afifi, Chant Avedissian, Mohamed Abla, Amr Kafrawy and Mona Marzouk.This paper deals with the impact of the modern Egyptian city of the contemporary Egyptian imaging through following five artists with different ages, educational backgrounds and methods of modern processors and contemporary paintings.

scholarly journals Diseño de una actividad didáctica con base en un diálogo entre TAD y APOEDesign of a didactic activity based on a dialogue between ATD and APOE

2020 ◽  
Vol 22 (4) ◽  
pp. 189-203
Author(s):  
Rita Vázquez-Padilla ◽  
María Trigueros ◽  
Avenilde Romo-Vázquez
Keyword(s):  
Linear Algebra ◽  
Reverse Transformation ◽  
Apos Theory ◽  
Modelling Activity ◽  
Anthropological Theory ◽  
Action Process

AbstractWe present the design of a modelling activity based on the dialogue between anthropological theory of the didactic (ATD) and the Action-Process-Object-Schema (APOS) theory. We focus in illustrating the potentiality of this dialogue for the design and analysis of research experiences.Palabras-clave: TAD, APOE, Modelación, Álgebra lineal; Transformación inversa.ResumenSe presenta el diseño de una actividad de modelación a partir del diálogo entre la teoría antropológica de lo didáctico (TAD) y la teoría Acción-Proceso-Objeto-Esquema (APOE). Nos centramos en ilustrar la potencialidad de dicho diálogo para el diseño y análisis de experiencias de investigación.Keywords: TAD, APOS, Modeling, Linear algebra; Reverse transformation.

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