**Course Description: **A public compulsory and a degree course open to all regular students who study nature science, especially science and engineering. The course is essential to these students seeking postgraduate study.

Linear algebra is a branch of mathematics dealing with matrices and vector spaces. Matrices have been introduced here as a handy tool for solving problems of linear algebra. Including: matrix algebra, determinants, vectors and vector spaces, linear systems of equations, eigenvalues and eigenvectors, quadratic forms.

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**Brief Introduction: **The students should familiarize with: Matrix operations, the three elementary operations and the steps for reducing a matrix to row echelon form by using elementary (row) operations. Computing the rank of a matrix. Finding the inverse of a matrix and remembering the properties of the inverse. Computing the determinants of numerical matrices and remembering the properties of determinants. Try to understand linear independence and linear dependence, which are central concepts in this course, and compute the rank of vectors’ group and find the basis of vector space. Solving a linear system. Remembering the properties of eigenvalues and eigenvectors and finding eigenvalues and eigenvectors of a matrix. Knowing the conditions of diagonalizable matrices and diagonalizing matrices. Writing the matrix of a quadratic form and changing of variable in a quadratic form that transforms the quadratic form into a standard form with no cross-product term.