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# NumPy | matmul Method

schedule Aug 12, 2023
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Numpy's matmul(~) method is used to perform compute the product of two arrays. These arrays can be vectors, matrices and even higher dimensions.

NOTE

matmul(~) is strikingly similar to Numpy's dot(~) method. The difference is as follows:

• matmul(~) does not support scalar multiplications, while dot(~) does.

• matmul(~) method is preferred over Numpy's dot(~) method when you need to perform matrix multiplication.

# Parameters

1. a | array_like

✜ The first argument.

2. b | array_like

✜ The second argument.

# Return value

The following table succinctly summaries what operation is performed as well as the return type:

a

b

operation

Return type

1D array

1D array

Vector dot product

number

2D array

1D array

Matrix-vector product

1D Numpy array

2D array

2D array

Matrix-matrix multiplication

2D Numpy array

n-D array

n-D array

Batch products

n-D Numpy array

# Examples

## Matrix-vector product

 x = [[1,0], [0,1]]y = [5,5]np.matmul(x,y) array([5, 5]) 

Mathematically, we're doing the following:

$$\begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 5\\ 5\\ \end{pmatrix}= \begin{pmatrix}5\\ 5\\ \end{pmatrix}$$

## Matrix-matrix product

 x = [[1,0], [0,1]]y = [[2,2], [2,2]]np.matmul(x,y) array([[2, 2], [2, 2]]) 

Mathematically, we're doing the following:

$$\begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 2&2\\ 2&2\\ \end{pmatrix}= \begin{pmatrix} 2&2\\ 2&2\\ \end{pmatrix}$$

Always remember that parameters just need to be array-like; we can use Numpy arrays as well:

 x = np.array([[1,0], [0,1]])y = np.array([[2,2], [2,2]])np.matmul(x, y) array([[2, 2], [2, 2]]) 

## Batch products

The matmul(~) method can be used to compute multiple products at once, like follows:

 x = [ [[1,0], [0,1]], [[1,1], [1,1]] ]y = [3,4]np.matmul(x,y) array([[3, 4], [7, 7]]) 

In this example, the variable x holds the following two matrices:

$$\begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} \;\;\;\; \begin{pmatrix} 1&1\\ 1&1\\ \end{pmatrix}$$

The final line, np.matmul(x,y), is performing the following mathematical operations:

$$\begin{pmatrix} 1&0\\ 0&1\\ \end{pmatrix} \begin{pmatrix} 3\\ 4\\ \end{pmatrix}= \begin{pmatrix} 3\\ 4\\ \end{pmatrix}$$
$$\begin{pmatrix} 1&1\\ 1&1\\ \end{pmatrix} \begin{pmatrix} 3\\ 4\\ \end{pmatrix}= \begin{pmatrix} 7\\ 7\\ \end{pmatrix}$$

Note that batch products also for vector-vector product and matrix-matrix product as wel

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