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# Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD

## Overview

In the first part of this course you will explore methods to compute an approximate solution to an inconsistent system of equations that have no solutions. Our overall approach is to center our algorithms on the concept of distance. To this end, you will first tackle the ideas of distance and orthogonality in a vector space. You will then apply orthogonality to identify the point within a subspace that is nearest to a point outside of it. This has a central role in the understanding of solutions to inconsistent systems. By taking the subspace to be the column space of a matrix, you will develop a method for producing approximate (“least-squares”) solutions for inconsistent systems.

You will then explore another application of orthogonal projections: creating a matrix factorization widely used in practical applications of linear algebra. The remaining sections examine some of the many least-squares problems that arise in applications, including the least squares procedure with more general polynomials and functions.

This course then turns to symmetric matrices. arise more often in applications, in one way or another, than any other major class of matrices. You will construct the diagonalization of a symmetric matrix, which gives a basis for the remainder of the course.

Greg Mayer

## Reviews

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• B. Malathi completed this course, spending 21 hours a week on it and found the course difficulty to be very hard.

The course contains basic ,innovative applied mathematical analysis.Also I thank to Georgia Institute of Technology via edX for that wonderful hours to learn Linear Algebra IV: Orthogonality & Symmetric Matrices and the SVD . When the course period the professors gave a perfect and dedication of their knowledge to improve improve the students talent ,activities,personal attitude,mentally fit ,bold ,talkative easily with others for subject basics to current affairs. I really thanks to my all professors .Teachers are not builders. they are creators. Once again I thanks to them for the wonderful hours spend with them.

Thank You.

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