Statistical Simulation for the Invertibility Test of Binary Random Matrices
Science Journal of Education
Volume 5, Issue 3, June 2017, Pages: 115-118
Received: Apr. 21, 2017; Published: Apr. 21, 2017
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Jing Yao, Department of Mathematics, Southern University of Science and Technology, Shenzhen, China
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One specific mathematical problem is discussed by combining the knowledge of statistical simulation and linear algebra. Aiming to solve this easy-to-understand yet hard-to-answer problem, this paper tries in two ways to test the invertibility of large random binary matrices. By generating random entries of the matrices, and using sparse sampling strategies to get matrices, we also consider programming techniques in order to break the bottleneck of computing power. The proportion of singular matrices changes with the increase of matrix order and the trend is presented. The advantages and disadvantages of the methods are also analyzed from the aspects of result accuracy, time efficiency and applicability. This paper is an example of computer-aided teaching to assist students in enhancing their understanding and practical ability.
Matrix Theory, Statistical Simulation, Sampling Strategy, College Mathematics Education
To cite this article
Jing Yao, Statistical Simulation for the Invertibility Test of Binary Random Matrices, Science Journal of Education. Vol. 5, No. 3, 2017, pp. 115-118. doi: 10.11648/j.sjedu.20170503.17
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