Eigenvalues and Eigenvectors: Understanding Matrix Properties

This lecture covers the concepts of eigenvalues and eigenvectors, essential in linear algebra. The instructor explains how to find eigenvalues by solving characteristic equations and how to determine eigenvectors by calculating the null space of the matrix. Through examples, the lecture demonstrates the process of finding eigenvalues and eigenvectors for different matrices, including triangular matrices. The lecture also explores the application of eigenvalues and eigenvectors in solving systems of linear equations and understanding Fibonacci sequences. By the end, the lecture presents a detailed derivation of a formula to calculate the nth Fibonacci number using eigenvalues and eigenvectors.