Applications of Linear Algebra

About this Professional Certificate

This certificate program will take students through roughly seven weeks of MATH 1554, Linear Algebra, as taught in the School of Mathematics at The Georgia Institute of Technology.

In the first course, you will explore the determinant, which yields two important results. First, you will be able to apply an invertibility criterion for a square matrix that plays a pivotal role in, for example, computer graphics and in other more advanced courses, such as multivariable calculus. The first course then moves on to eigenvalues and eigenvectors. The goal of this part of the course is to decompose the action of a linear transformation that may be visualized. The main applications described here are to discrete dynamical systems, including Markov chains. However, the basic concepts afforded by eigenvectors and eigenvalues are useful throughout industry, science, engineering and mathematics.

In the second course you will explore methods to compute an approximate solution to an inconsistent system of equations that have no solutions. This has a central role in the understanding of current data science applications. The second course then turns to symmetric matrices. They arise often in applications of the singular value decomposition, which is another tool often found in data science and machine learning.

What you'll learn

• Model and solve real-world problems using Markov chains, determinants, dynamical systems, and Google Page Rank.
• Construct the singular value decomposition (SVD) of a matrix and apply the SVD to estimate the rank and condition number of a matrix, construct a basis for the four fundamental spaces of a matrix, and construct a spectral decomposition of a matrix.
• Apply the iterative Gram Schmidt Process and the QR decomposition to construct an orthogonal basis of a subspace.
• Apply least-squares and multiple regression to construct a linear model from a data set.
• Apply eigenvalues and eigenvectors to solve optimization problems that are subject to distance and orthogonality constraints.

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