 Last Updated on March 12, 2023 by Umer Malik

Very loosely stated, linear algebra is the study of linear equations and linear transformations. It was initially driven by the former but has gradually changed to focus more on the latter since it turns out that this is what should be studied. There are several significant instances of linear transformations, including scaling by a fixed constant, derivatives, and rotations around a defined origin.

Reasons Why you Should use Linear Algebra in Quantitative Finance

1)    It tends to be considerably broader than one may initially think it should be. For instance, it has some rather fundamental connections to number theory. Additionally, it is crucial for things like Markov chains, which powers Google search and predictive text, and machine learning.

2)    It has been extensively researched. There are several efficient methods for carrying out various linear algebra-related activities. Therefore, if you can simplify your issue to a linear algebraic equation, there is a strong likelihood that someone has already done so, or at the very least has given you the necessary tools to figure it out independently.

## Linear Algebra in Machine Learning

Computers and machines can only comprehend numbers. Furthermore, these figures must be expressed and handled in a way that enables machines to solve issues by learning from the data rather than by following predetermined instructions.

Model training in machine learning is the process of using data to determine the appropriate parameters for a function. As a result, machine learning may be summarised as programming that seeks to optimise for the best possible answer. linear algebra is the first step in mastering math for machine learning.

## Uses of Linear Algebra in Quantitative Finance and Machine Learning

1)    Creating Datasets

Using a dataset, you fit a model in machine learning. This is a set of integers that resembles a table, with each row denoting an observation and each column denoting a feature of that observation.

In addition, you have an X matrix and a V vector when you divide the data into inputs and outputs to construct a machine learning model. Another important data unit in linear algebra is the vector.

2)    Encoding

In machine learning, categorical data is occasionally used. It might be categorical input data or class labels for classification issues. Categorical variables are frequently encoded to make them simpler to use and understand via certain methods.  ‘One hot’ encoding is a well-known categorical variable encoding.

3)    ‘Deep Learning’

Deep learning is the current upsurge in the usage of artificial neural networks, which enables the building and training of larger and deeper networks on very large datasets using newer techniques and faster technology.

Neural networks operate primarily by multiplying and averaging data structures from linear algebra.

## Learning about Financial Linear Algebra

One of the best ways to develop in your job and acquire the theories that make up financial mathematics, such as linear algebra, is to enrol in a specialised financial mathematics course like the Certificate in Quantitative Finance (CQF). With the aid of such courses, a person with the required qualifications can progress in their career or even change to a higher paid job.