18.06 | Spring 2010 | Undergraduate

Linear Algebra

Video Lectures

Lecture 27: Positive definite matrices and minima

In calculus, the second derivative decides whether a critical point of y(x) is a minimum. For functions of multiple variables, the test is whether a matrix of second derivatives is positive definite. In this session we learn several ways of testing for positive definiteness and also how the shape of the graph of ƒ(x) = x_T_Ax is determined by the entries of A.

These video lectures of Professor Gilbert Strang teaching 18.06 were recorded in Fall 1999 and do not correspond precisely to the current edition of the textbook. However, this book is still the best reference for more information on the topics covered in each lecture.

Strang, Gilbert. Introduction to Linear Algebra. 5th ed. Wellesley-Cambridge Press, 2016. ISBN: 9780980232776.

Instructor/speaker: Prof. Gilbert Strang

Course Info

As Taught In
Spring 2010
Learning Resource Types
Lecture Videos
Problem Sets with Solutions
Exams with Solutions
Instructor Insights