In Python, the error `ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?)`

arises when attempting matrix multiplication and the dimensions of the matrices are not aligned correctly according to the rules of matrix multiplication.

In matrix multiplication, if you have two matrices `A`

and `B`

, the number of columns in `A`

must match the number of rows in `B`

. Otherwise, Python raises a `ValueError`

, as it cannot perform the operation due to dimensional mismatch.

We will go through an example and how to solve it.

## Error Explanation

The error looks a bit scary, but let’s break it into smaller pieces to help you understand what’s going on!

ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?)

`matmul`

: Refers to matrix multiplication using`numpy.matmul`

or the`@`

operator.`Input operand 1 has a mismatch in its core dimension 0`

: Operand 1 refers to the second matrix, and its first dimension (rows) is incompatible with the first matrix’s second dimension (columns).`gufunc signature (n?,k),(k,m?)->(n?,m?)`

: This signature indicates the expected dimensions for matrix multiplication, where the number of columns in the first matrix (k) must match the number of rows in the second matrix (k).

## Example

import numpy as np # Define two incompatible matrices A = np.array([[1, 2, 3], [4, 5, 6]]) # Shape: (2, 3) B = np.array([[1, 2], [3, 4]]) # Shape: (2, 2) # Attempting matrix multiplication result = A @ B

When you run this code, Python will raise the following error:

ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 2 is different from 3)

For matrix multiplication to be valid:

- The number of
**columns**in the first matrix (`A`

) must be equal to the number of**rows**in the second matrix (`B`

).

The matrix `A`

has a shape of `(2, 3)`

(two rows, three columns), and the matrix `B`

has a shape of `(2, 2)`

(two rows, three columns). Since the number of columns in `A`

(3) does not match the number of rows in `B`

(2), this results in the `ValueError`

.

### Solution

To fix this error, ensure that the dimensions of the two matrices are compatible for matrix multiplication. In this case, you need to modify `B`

so that its number of rows matches the number of columns in `A`

.

Here’s how you can adjust the matrices to make them compatible:

import numpy as np # Define compatible matrices A = np.array([[1, 2, 3], [4, 5, 6]]) # Shape: (2, 3) B = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) # Shape: (3, 3) # Perform matrix multiplication result = A @ B print(result)

**Output:**

[30 36 42] [66 81 96]]

Now, matrix `A`

has a shape of `(2, 3)`

and matrix `B`

has a shape of `(3, 3)`

, making them compatible for matrix multiplication. The resulting matrix will have a shape of `(2, 3)`

.

### General Approach to Fixing This Error

**Check the dimensions**: Ensure the number of columns in the first matrix equals the number of rows in the second matrix.**Reshape or slice matrices**: If necessary, reshape or slice the matrices to ensure compatibility.**Transpose if needed**: In some cases, transposing one of the matrices can fix the issue, but please ensure this matches your computation’s logic.

### Example Where Transposing is Necessary

Sometimes, the structure of the matrices cannot be directly aligned for matrix multiplication, but by transposing one of the matrices, you can make them compatible.

Let’s look at an example:

import numpy as np # Define two incompatible matrices A = np.array([[1, 2], [3, 4], [5, 6]]) # Shape: (3, 2) B = np.array([[1, 2, 3], [4, 5, 6]]) # Shape: (2, 3) # Attempting matrix multiplication result = A @ B print(result)

**Output:**

[[ 9 12 15] [19 26 33] [29 40 51]]

However, let’s modify matrix `B`

to make them incompatible by changing its shape to `(3, 2)`

:

import numpy as np # Define two incompatible matrices A = np.array([[1, 2], [3, 4], [5, 6]]) # Shape: (3, 2) B = np.array([[1, 2], [3, 4], [5, 6]]) # Shape: (3, 2) # Attempting matrix multiplication (this will raise an error) result = A @ B

This raises the familiar error:

ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0, with gufunc signature (n?,k),(k,m?)->(n?,m?) (size 3 is different from 2)

Here, matrix `A`

has 2 columns, but matrix `B`

has 3 rows, which makes them incompatible for multiplication.

#### Solution: Transposing the Matrix

By transposing matrix `B`

, we can make the shapes compatible for matrix multiplication:

import numpy as np # Define two matrices A = np.array([[1, 2], [3, 4], [5, 6]]) # Shape: (3, 2) B = np.array([[1, 2], [3, 4], [5, 6]]) # Shape: (3, 2) # Transpose matrix B to make the shapes compatible B_T = B.T # Shape: (2, 3) # Perform matrix multiplication result = A @ B_T print(result)

After transposing `B`

, it now has a shape of `(2, 3)`

, which is compatible with `A`

‘s shape of `(3, 2)`

. The output will be:

[[ 5 11 17] [11 25 39] [17 39 61]]

The `ValueError: matmul: Input operand 1 has a mismatch in its core dimension 0`

error typically occurs due to incompatible matrix shapes. By checking and adjusting the dimensions of your matrices, you can resolve this error and successfully perform matrix multiplication.

Congratulations on reading to the end of this tutorial!

For further reading on NumPy arrays, go to the article: How to Solve Python ValueError: operands could not be broadcast together with shapes

Have fun and happy researching!

Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.