Matrix analysis is a branch of mathematics that focuses on the study of matrices, which are rectangular arrays of numbers or symbols. It involves various operations such as addition, multiplication, and finding determinants, which help in solving systems of linear equations. Matrix analysis is widely used in fields like engineering, computer science, and economics to model and analyze complex data. In addition to basic operations, matrix analysis explores properties like eigenvalues and eigenvectors, which provide insights into the behavior of linear transformations. This makes it a powerful tool for applications such as machine learning, statistics, and quantum mechanics, where understanding relationships between variables is crucial.