Lecture3 - CS 435 Linear Optimization Fall 2008 Lecture 3 Linear Algebra Basics Lecturer Sundar Vishwanathan Computer Science& Engineering

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Unformatted text preview: CS 435 : Linear Optimization Fall 2008 Lecture 3: Linear Algebra Basics Lecturer: Sundar Vishwanathan Computer Science & Engineering Indian Institute of Technology, Bombay Last time we saw how to solve a system of linear equations. To understand what the set of all solutions look like, we need some vocabulary. This comes from Linear Algebra. We need to wade through a few de nitions rst. Most abstract algebraic objects have sets and operations de ned on them. Our object of interest is a vector space, which comes with two sets (both in nite) with operations. To most of you mention of a vector space would conjure a set with objects which look like (3 ; 4 : 55 ; : 76 ; ; : : : ; 4) T . We do not wish to disturb this. Indeed, we will get to this picture very soon. We wish to point out that the subject of linear algebra can be developed without explicit co-ordinates and we will tread this path initially. 1 Vector Space A vector space is de ned as a set of vectors V and the real numbers R (called scalars ) with the following operations de ned:...
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This note was uploaded on 01/04/2010 for the course CSE CS435 taught by Professor Profsundar during the Summer '09 term at IIT Bombay.

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Lecture3 - CS 435 Linear Optimization Fall 2008 Lecture 3 Linear Algebra Basics Lecturer Sundar Vishwanathan Computer Science& Engineering

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