So just like that, using the information that we proved to ourselves in the last video, we're able to figure out that the two eigenvalues of A are lambda equals 5 and lambda equals negative 1. …

If you take one of these eigenvectors and you transform it, the resulting transformation of the vector's going to be minus 1 times that vector. Anyway, we now know what eigenvalues, …

We figured out the eigenvalues for a 2 by 2 matrix, so let's see if we can figure out the eigenvalues for a 3 by 3 matrix. And I think we'll appreciate that it's a good bit more difficult …

Eigenvalues are one part of a process that leads (among other places) to a process analogous to prime factorization of a matrix, turning it into a product of other matrices that each have a set …

If A is an nxn matrix, then the equation Ax=b gives us n equations (one for each row of A) in n+1 unknowns (the n dimensional variables plus lambda). Since the solution is not unique (as there …

For a given operation matrix A, we are able to find eigenvalues and eigenvectors and hence form an eigenspace. Can you please give an example in physics or signal processing which could …

By capturing all the second-derivative information of a multivariable function, the Hessian matrix often plays a role analogous to the ordinary second derivative in single variable calculus.

This topic covers: - Adding & subtracting matrices - Multiplying matrices by scalars - Multiplying matrices - Representing & solving linear systems with matrices - Matrix inverses - Matrix …

Manually finding the determinants or inverses of higher dimension matrices is a lot harder than 2x2 matrices. If you are asked to do so for very high dimension matrices, it'll probably be with …

Unit 2: Matrix transformations About this unit Matrices can be used to perform a wide variety of transformations on data, which makes them powerful tools in many real-world applications. For …