Скачать или смотреть How to Invert a Matrix of Fractions with NumPy Using SymPy

Learn how to easily invert matrices containing `Fraction` objects in Python by using SymPy, overcoming common limitations faced with NumPy.
---
This video is based on the question https://stackoverflow.com/q/65164336/ asked by the user 'DaraJ' ( https://stackoverflow.com/u/589921/ ) and on the answer https://stackoverflow.com/a/65165210/ provided by the user 'hpaulj' ( https://stackoverflow.com/u/901925/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

Visit these links for original content and any more details, such as alternate solutions, latest updates/developments on topic, comments, revision history etc. For example, the original title of the Question was: Invert matrix of Fractions with numpy

Also, Content (except music) licensed under CC BY-SA https://meta.stackexchange.com/help/l...
The original Question post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license, and the original Answer post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license.

If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com.
---
How to Invert a Matrix of Fractions with NumPy Using SymPy

In the world of programming and data science, handling matrices efficiently is a common requirement, especially when dealing with mathematical computations. A common issue arises when attempting to invert a matrix that contains fractions using popular libraries like NumPy. If you've encountered errors while using NumPy with Fraction objects, you're not alone.

The Problem: Inverting a Matrix of Fractions

Suppose you have an n*n matrix defined like this:

[[See Video to Reveal this Text or Code Snippet]]

When you attempt to find its inverse using the NumPy library with the following code:

[[See Video to Reveal this Text or Code Snippet]]

You might come across an error message saying:

[[See Video to Reveal this Text or Code Snippet]]

This is a common limitation when working with NumPy, which does not support matrices containing Fraction objects directly.

The Solution: Using SymPy for Fractional Matrices

The good news is there’s a straightforward workaround! By using the SymPy library, you can compose and manipulate matrices containing fractions seamlessly.

Step 1: Import Necessary Libraries

First, ensure you have SymPy installed. You can easily install it using pip:

[[See Video to Reveal this Text or Code Snippet]]

Now, let's import the required components from SymPy:

[[See Video to Reveal this Text or Code Snippet]]

Step 2: Define Your Matrix

Now it’s time to create your matrix using SymPy’s Matrix and Rational classes. This allows you to handle fractional values properly:

[[See Video to Reveal this Text or Code Snippet]]

Step 3: Invert the Matrix

You can then easily compute its inverse:

[[See Video to Reveal this Text or Code Snippet]]

The output will be:

[[See Video to Reveal this Text or Code Snippet]]

Step 4: Validating the Result

You can compare your results by also computing the inverse with floating-point numbers to ensure accuracy:

Create a float matrix:

[[See Video to Reveal this Text or Code Snippet]]

Compute its inverse:

[[See Video to Reveal this Text or Code Snippet]]

You can also check that both inverses are equivalent when scaled:

[[See Video to Reveal this Text or Code Snippet]]

Conclusion

By switching from NumPy to SymPy, you can easily invert matrices that contain fractional values. Not only does this avoid the pitfalls of type errors in NumPy, but it also expands your capabilities in mathematical computations involving rational numbers.

Armed with this knowledge, you can now confidently work with matrices of fractions in Python!