A Study of Advancement of Linear Algebra for the Future Analysis

Exploring the Applications and Theory of Linear Algebra in Future Analysis

Abstract

Analytical applications for Big Data future analysis frequently make use of linear algebraconcepts like linear equations, eigenvalue problems, principal component analysis, singular valuedecomposition, quadratic forms, linear inequalities, linear programming, optimization, linear differentialequations, modeling, prediction, and data mining algorithms. Solving linear equations, multiplying andinverting matrices, computing and interpreting determinants, locating eigenvalues and eigenvectors, andso on are all examples of the computational techniques that make up one branch of linear algebra.Meanwhile, linear algebra also has a theoretical component that deals with things like abstract vectorspaces, subspaces, linear independence, spanning sets, bases, dimension, and linear transformations.To go into several cutting-edge areas of linear algebra that reveal the various ways in which this field ofstudy is related to other branches of mathematics. Large-scale network analysis, Leontief economicmodels which assume that consumption equals output on a nationalregional scale and sports teamrankings all make heavy use of linear equations and matrices in Future Analysis.