Cover Image

Scrutiny of Academic Performance of Students using Eigenvalue and Eigenvectors: A case study

Muhammad Afzal Sahito, Feroz Shah, Asif Ali Shaikh

Abstract


In this paper we are significantly concerned with the students’ academic performance. Although, this is significantly considered the important of academics with mathematically and principal component analysis(PCA). The eigenvalue problems arise in a variety of science and engineering applications and in the past two decades many developments have been done by numerical methods. The study of students’ academic performance of different subjects and derive results for the ordered eigenvalues and corresponding eigenvectors. The main results are showing that solutions of the students marks that can be expressed two batches and four semesters, as functions of eigenvalue and eigenvectors of the covariance matrix. Moreover, under an assumption for the eigenvalue of covariance matrix of the different subject’s marks and positive solutions are characterized by eigenvalues and eigenvectors.

Full Text:

PDF

References


ABRO, S., MA SOLANGI, and AA SHAIKH. "An Investigation on the Performance of Students in Mathematics: A Case Study." Sindh University Research Journal-SURJ (Science Series) 48.2 (2016).

Alaíz, Carlos M., Michaëel Fanuel, and Johan AK Suykens. "Convex formulation for kernel PCA and its use in semisupervised learning." IEEE transactions on neural networks and learning systems (2017).

Bunea, Florentina, and Luo Xiao. "On the sample covariance matrix estimator of reduced effective rank population matrices, with applications to fPCA." Bernoulli 21.2 (2015): 1200-1230

Di Napoli, Edoardo, Eric Polizzi, and Yousef Saad. "Efficient estimation of eigenvalue counts in an interval." Numerical Linear Algebra with Applications 23.4 (2016): 674-692. [5] Lee, Ching-Yi, and Hsin-Yi Kung. "Math Self-Concept and Mathematics Achievement: Examining Gender Variation and Reciprocal Relations among Junior High School Students in Taiwan." Eurasia Journal of Mathematics, Science and Technology Education 14.4 (2018): 1239-1252.

Lee, Ji Oon, and Kevin Schnelli. "Extremal eigenvalues and eigenvectors of deformed Wigner matrices." Probability Theory and Related Fields 164.1-2 (2016): 165-241.

Pirani, Mohammad, and Shreyas Sundaram. "On the smallest eigenvalue of grounded Laplacian matrices." IEEE Transactions on Automatic Control 61.2 (2016): 509-514.


Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 University of Sindh Journal of Information and Communication Technology



ISSN-E: 2523-1235, ISSN-P: 2521-5582

 Copyright © University of Sindh, Jamshoro. 2017 All Rights Reserved.  
Printing and Publication by: Sindh University Press. 


Journal Office, Institute of Information and Communication Technology, 
University of Sindh, Jamshoro, Sindh, Pakistan. 76080