Video details loadedContinue
HomeMIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018Lecture 5: Positive Definite and Semidefinite Matrices
MIT 18.065 Matrix Methods in Data Analysis, Signal Processing, and Machine Learning, Spring 2018
Video 7 of 10
Lecture 5: Positive Definite and Semidefinite Matrices
45:27
Up Next
Lecture 6: Singular Value Decomposition (SVD)
Description
In this lecture, Professor Strang continues reviewing key matrices, such as positive definite and semidefinite matrices. This lecture concludes his review of the highlights of linear algebra.
SummaryAll eigenvalues of S are positive.
Energy x_T_Sx is positive for x \(\neq 0\).
All pivots are positive S = A_T_A with independent columns in A.
All leading determinants are positive 5 EQUIVALENT TESTS.
Second derivative matrix is positive definite at a minimum point.
Semidefinite allows zero evalues/energy/pivots/determinants.
Related section in textbook: I.7
Instructor: Prof. Gilbert Strang
