The Matrices Which are Usually Unusual - Idempotent, Involutory, Nilpotent Matrix

What is Metrix? Matrix is an arrangement of numbers into rows and columns. ... A matrix is a rectangular arrangement of numbers into rows and columns. For example, matrix A has two rows and three columns. Idempotent Matrix: An idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix A is idempotent if and only if A^{2}=A. For this product A^{2} to be defined, A must necessarily be a square matrix. Viewed this way, idempotent matrices are idempotent elements of matrix rings. Involutory Matrix: An involutory matrix is a matrix that is its own inverse. That is, multiplication by matrix A is an involution if and only if A^2 = I. Involutory matrices are all square roots of the identity matrix. This is simply a consequence of the fact that any non-singular matrix multiplied by its inverse is the identity. Nilpotent Matrix: A nilpotent matrix is a square matrix N such that N^{k}=0, for some positive integer k. The smallest such k is called the index of N, sometimes the degree of N. #Matrix Watch the video and Learn Something Extraordinary... Subscribe: BRAIN EXPLODERS Link: https://www.youtube.com/c/BrainExploders A challenge for you in the last of this videos of the playlist Exploders Contest, can you solve that questions? Watch the videos, Take your time & give your answer in the comment section, if your answer is correct, we'll announce your name in our next YouTube video of this playlist - Exploders Contest: Season 2. Season 2 Link: https://www.youtube.com/watch?v=pkCfzZKi-50&list=PL8o2Zp8DZECwLeQEoAQh2sVxDPL6PVKqm Suggested Book: Title: Introduction to Applied Linear Algebra: Vectors, Matrices, and Least Squares Link: https://amzn.to/2DV0ULT Exploders Contest: Season 1 Link: https://www.youtube.com/playlist?list=PL8o2Zp8DZECwfB_vjo8Kc-HxB23JJgnwW This is the channel to feature this type of questions suggested by the people. Join us on another platforms Instagram: https://www.instagram.com/brain_exploders/ Facebook: https://www.facebook.com/brainexploders Messenger: https://www.m.me/brainexploders Twitter: https://twitter.com/BrainExploders Telegram: https://t.me/Brain_Exploders ___Show your support to us. ________THANKS FOR WATCHING #Brain_Exploders _______________Next video will come soon.