From the course: Machine Learning Foundations: Linear Algebra
Join today to access over 23,200 courses taught by industry experts.
Changing to the eigenbasis
From the course: Machine Learning Foundations: Linear Algebra
Changing to the eigenbasis
- [Instructor] There are many applications in which we have to calculate high powers of square matrix A. What it basically means is that we have to apply the same matrix multiplication many times. We will explore that the most efficient way to calculate A to the power of n, especially for the larger values of n, is to first diagonalize A. Diagonalizing a matrix involves finding its eigenvalues and eigenvectors, and we have to find out how these values are related to those of A to the power of n. Let's Look at a simple example. We have a transformation matrix T that will represent rotation and shift of a vector v. We get the result of applying the transformation T on a vector v by multiplying the T with v, and we get a new vector, and let's call it v1. If we apply the transformation T on the vector v1, we get a new vector v2. We can conclude that this is equal to multiplying the transformation T twice with vector v. So, we…
Practice while you learn with exercise files
Download the files the instructor uses to teach the course. Follow along and learn by watching, listening and practicing.
Download courses and learn on the go
Watch courses on your mobile device without an internet connection. Download courses using your iOS or Android LinkedIn Learning app.