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Explore the fundamental properties of positive semi-definite matrices in this 24-minute lecture that examines how eigenvalues behave when these matrices are partitioned into blocks. Learn why eigenvalues of positive semi-definite matrices are always non-negative and discover the mathematical relationship between the largest eigenvalue of a PSD matrix and the eigenvalues of its constituent blocks. Gain insights into matrix theory concepts that are essential for understanding optimization, numerical analysis, and various applications in engineering and mathematics.
Syllabus
Positive semi-definite matrices and the eigenvalues of their partitioned form
Taught by
NPTEL-NOC IITM