Matrix is an arrangement of numbers into rows and columns. Make your first introduction with matrices and learn about their dimensions and elements. A matrix is a rectangular arrangement of numbers …

And all of that is really just matrix multiplication. So all of these things that you're doing in your fancy 3D games on your Xbox or your Playstation, they're all just matrix multiplications. And I'm going to prove …

An introduction to how the jacobian matrix represents what a multivariable function looks like locally, as a linear transformation.

But if matrix A is not a square matrix, then these are going to be two different identity matrices, depending on the appropriate dimensions. Now, let's see if we can extend this analogy between …

So you're not just blindly doing some-- matrix-matrix products can be pretty tedious, but now you know what they're for. They're actually for the composition of two transformations where each of A and B …

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

We're going to get a 3 by 1 matrix, which makes complete sense because we're dealing in R3. a is going to be member of R3. So when we write it with standard coordinates, we should have 3 coordinates …

Now that we know what a matrix is, let's see if we can start to define some operations on matrices. So let's say I have the 2 by 3 matrix, so two rows and three columns, and the entries are 7, 5, negative …

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.

Learn how to perform the matrix elementary row operations. These operations will allow us to solve complicated linear systems with (relatively) little hassle!