W4_L8: Eigenvalues & eigenvectors of an operator & its adjoint

Welcome to Week 4 Lecture 8 of the course "Maths for Electronics 2" by Prof. Andrew Thangaraj. Full Course: https://study.iitm.ac.in/es/course_pa... Video Overview In this lecture, we explore the deep connections between a linear operator and its adjoint by examining their eigenvalues and eigenvectors. We discuss how adjoints give rise to left and right eigenvectors, expanding our understanding of fundamental subspaces. We then establish the relationship between the eigenvalues of an operator and those of its adjoint, and highlight the orthogonality relation for eigenvectors. This lecture provides a clear explanation of the crucial links between eigenvalues, eigenvectors, and adjoint operators, building a strong foundation for advanced linear algebra. About IIT Madras' online Bachelor of Science programme IIT Madras offers four-year BS programmes that aim to provide quality education to all, irrespective of age, educational background, or location. The BS programme has multiple levels, which provide flexibility to students to exit at any of these levels. Depending on the courses completed and credits earned, the learner can receive a Foundation Certificate from IITM CODE (Centre for Outreach and Digital Education), Diploma(s) from IIT Madras, or BSc/BS Degrees from IIT Madras. For more details visit https://www.iitm.ac.in/academics/stud... #adjoint #operator #linearalgebra #eigenvalues #eigenvectors #hermitian #leftEigenvectors #rightEigenvectors #conjugate #orthogonal #math #mathematics #lecture #lineartransformation #STEM #EngineeringMath #AppliedMathematics #Tutorial