Unlocking the Mysteries of Special Matrices: Idempotent, Involutory, and Nilpotent 🧮

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.