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# NumPy | cross method

schedule Aug 11, 2023
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Numpy's `cross(~)` method computes the cross product of two input arrays.

# Parameters

1. `a` | `array-like`

The first input array.

2. `b` | `array-like`

The second input array.

3. `axisa` | `int` | `optional`

The axis along which to use to compute the cross product for array `a`. You only need to consider this if you're dealing with multi-dimensional arrays (e.g. 2D arrays). By default, the last axis will be used.

4. `axisb` | `int` | `optional`

The axis along which to use to compute the cross product for array `b`. You only need to consider this if you're dealing with multi-dimensional arrays (e.g. 2D arrays). By default, the last axis will be used.

# Return value

A Numpy array that represents the cross product of the two input arrays.

# Examples

## Basic usage

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

## Cross product of size-two arrays

We can also compute the cross product of arrays of size two:

``` x = [1, 2]y = [3, 4]np.cross(x,y) array(-2) ```

Here, we've computed the dot product `(1*4)-(2*3)=-2`.

## Cross products of size-two array and size-three array

``` x = [1, 2, 3]y = [4, 5]np.cross(x,y) array([-15, 12, -3]) ```

Here, `y` is assumed to be `[4, 5, 0]`, that is, the z-component is padded with 0.

## Cross products of 2D arrays

``` x = [[1,2,3], [4,5,6]]y = [[5,6], [7,8], [9,10]]np.cross(x, y, axisa=1, axisb=0) # axis=1 <- row wise, axis=0 <- column-wise array([[-3, 6, -3], [ 2, -4, 2]]) ```

To make it easier for your eyes, here's `x` and `y` prettified:

``` x = [[1, 2, 3], y = [[5, 6] [4, 5, 6]] [7, 8] [9, 10]] ```

What we've done here is computed the following:

``` np.cross([1,2,3], [5,7,9]) # [-3, 6, -3]np.cross([4,5,6], [6,8,10]) # [ 2, -4, 2] ```
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