Some of the operations have been included without using the numpy library. Description of issue being adressed and the solution approach are mentioned underneath ...

Sparse matrices are data structures that efficiently store and operate on matrices with mostly zero elements. They are crucial in machine learning for handling large datasets with many zero values, ...

Python is convenient and flexible, yet notably slower than other languages for raw computational speed. The Python ecosystem has compensated with tools that make crunching numbers at scale in Python ...