# Eigenvector

## Definition of Eigenvector

Eigenvector: An eigenvector is a particular type of vector that has a special property: it’s multiplied by a certain matrix (the “eigenvalue matrix”) in such a way that the result is always the same.

## What is an Eigenvector used for?

An Eigenvector is a special type of vector used in linear algebra and machine learning. It is often used to represent the direction of maximum variance within a set of data points. In other words, it can be used to identify the most important features within a dataset. An Eigenvector can also be used to find the principal components of a matrix, where it will reveal the underlying structure of the data. Additionally, it is widely used in unsupervised learning algorithms such as Principal Component Analysis (PCA) and Singular Value Decomposition (SVD). These methods allow for dimensionality reduction by taking a high-dimensional dataset and representing it with fewer dimensions while preserving as much information as possible. It has also been successfully applied to image processing, audio recognition, natural language processing, clustering analysis and network analysis. Finally, an eigenvector is also commonly used for classification tasks in supervised learning models such as support vector machines (SVMs).