Let's try out an example to demonstrate how we use matrices. This example uses matrices to interpolate a curve between a given set of points. Suppose we have a given set of points representing some data. The objective is to trace a smooth line between the points in order to produce a curve that estimates the shape of the data. Although the mathematical formulae in this example may seem difficult, we should know that this technique is actually just a form of regularization for a linear regression model, and is termed as **Tichonov regularization**. For now, we'll focus on how to use matrices in this technique, and we shall revisit regularization in depth in Chapter 2, *Understanding Linear Regression*.

We will first define ...

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