In this section, we'll start our discussion by explaining a matrix. A matrix from a mathematical perspective, is a 2-dimensional array that contains numbers. These numbers could be either real or complex. Matrices are universally applicable mathematical entities that find extensive use in areas such as physics and engineering. In Python, the Numpy library significantly simplifies the handling of matrices.

But why are matrices so fundamentally important in data science and machine learning? Consider an image. For humans, it's a visual depiction of an object or a scene. However, the image is an array of pixel values to a computer, making it a matrix. For tasks like image recognition, these matrices undergo processing and analysis. Thus, understanding how to manipulate matrices is invaluable for any data scientist or machine learning engineer.

To get started, let's import the Numpy library:

With Numpy, we can effortlessly create a matrix using the array function. We simply need to provide a 2-dimensional list as a parameter:

In the above snippet, A is a 3x3 matrix comprising three rows and three columns. Each row can be conceptualized as a 3-dimensional vector with every number acting as a coordinate in 3-dimensional space.

One admirable aspect of matrices is the intuitive way they can be manipulated. Operations such as addition, subtraction, and multiplication are carried out element-wise, i.e., on corresponding elements from each matrix. This greatly simplifies the task of performing these operations, which could be considerably more complex in higher dimensions.