# Linear Algebra used in Machine Learning

Linear algebra is a branch of mathematics that is widely used throughout science and engineering. Yet because linear algebra is a form of continuous rather than discrete mathematics, many computer scientists have little experience with it.

A good understanding of linear algebra is essential for understanding and working with many machine learning algorithms, especially deep learning algorithms. We therefore precede our introduction to deep learning with a focused presentation of the key linear algebra prerequisites.

## Vectors, Matrices and Tensors

In machine learning, the majority of data is most often represented as vectors, matrices or tensors. Therefore, the machine learning heavily relies on the linear algebra.

**A vector**is a 1D array. For instance, a point in space can be defined as a vector of three coordinates (*x*,*y*,*z*). Usually, it is defined in such a way that it has both the magnitude and the direction.**A matrix**is a two-dimensional array of numbers, that has a fixed number of rows and columns. It contains a number at the intersection of each row and each column. A matrix is usually denoted by square brackets [].**A tensor**is a generalization of vectors and matrices. For instance, a tensor of dimension one is a vector. In addition, we can also have a tensor of two dimensions which is a matrix. Then, we can have a three-dimensional tensor such as the image with RGB colors. This continues to expand to four-dimensional tensors and so on.

Furthermore, many operations can be applied on them like **addition**, **subtraction**, **multiplication**, etc.

# Applications of Linear Algebra

Thank you for reading! I would appreciate any comments, notes, corrections, questions or suggestions — if there’s anything you’d like me to write about, please don’t hesitate to let me know.