# Linear Algebra

Linear algebra is study of linear systems of equations and their transformation properties.

Linear algebra is a college-level concept and course.

### Prerequisites

Lie Group: | A Lie group is a differentiable manifold that has the structure of a group and that satisfies the additional condition that the group operations of multiplication and inversion are continuous. |

Linear Transformation: | A function from one vector space to another. If bases are chosen for the vector spaces, a linear transformation can be given by a matrix. |

Matrix: | A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, for every linear transformation, there exists exactly one corresponding matrix, and every matrix corresponds to a unique linear transformation. The matrix is an extremely important concept in linear algebra. |

Vector: | (1) In vector algebra, a vector mathematical entity that has both magnitude (which can be zero) and direction. (2) In topology, a vector is an element of a vector space. |

Vector Space: | A vector space is a set that is closed under finite vector addition and scalar multiplication. The basic example is n-dimensional Euclidean space. |