Given 2 arrays create a Cauchy matrix from it?
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# Given 2 arrays create a Cauchy matrix from it?

Given 2 arrays create a Cauchy matrix from it

## Recipe Objective

A Cauchy matrix is a matrix determined by two vectors. Given two vectors x and y, the Cauchy matrix C generated by them is defined as: C[i][j] := 1/(x[i] - y[j]). Now, we can use for loop to create it but let's look at an efficient way.

So this recipe is a short example on how to create a Cauchy matrix from two arrays. Let's get started.

## Step 1 - Import the library

``` import numpy as np ```

Let's pause and look at these imports. Numpy is generally helpful in data manipulation while working with arrays. It also helps in performing mathematical operation.

## Step 2 - Generating two arrays

``` x = np.array([1,2,3,4]) y = np.array([5,6,7]) ```

Here, we have created two simple arrays.

## Step 3 - Generating Cauchy matrix

``` c= 1.0 / (x.reshape((-1,1)) - y) ```

Now, using the formula, we have created a simple cauchy matrix.

## Step 4 - Printing the nearest value

``` print(c) ```

Now, simply using print function, we have print our matrix.

## Step 5 - Let's look at our dataset now

Once we run the above code snippet, we will see:

```Scroll down the ipython file to visualize the output.
```

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