Linear algebra is a branch of mathematics that deals with the study of linear equations and linear transformations. It is a fundamental mathematical tool for many areas of science and engineering, including machine learning, computer graphics, computer vision, and data analysis.

At its core, linear algebra is concerned with the manipulation of vectors and matrices. A vector is a mathematical object that has both magnitude (size) and direction, and it can be represented as a list of numbers. A matrix is a rectangular array of numbers, and it is used to represent linear transformations, which are functions that take one vector as input and produce another vector as output.

Linear algebra has many practical applications, including finding solutions to systems of linear equations, computing the rank of a matrix, determining the eigenvalues and eigenvectors of a matrix, and performing singular value decomposition (SVD). It is also an important tool for understanding more advanced mathematical concepts, such as multivariate calculus and differential equations.