（课程简介英文版） The main contents of this course include linear algebra theory determinant, linear equations, matrix, quadratic, linear space, linear transformations and Euclidean space, etc. Specifically, this course includes the following contents: factorization of polynomial and the fundamental theorem of algebra; the definition of determinant and the method of calculating the determinant, Cramer rule; vector space, linear correlation of vector, solvable discriminate theorem of linear equations, solution’s structure of linear equations; concept and operation of matrix, inverse matrix and the matrix equation; standard form and unique of quadratic form, positive definite quadratic form; concept of linear space, dimension, basis and coordinate of linear space, basis transformation and coordinate transformation formula, linear subspace, isomorphism of linear space; Matrix of linear transformation, eigenvalue and eigenvector of linear transformation, diagonalization of matrices; Euclidean space, normal orthogonal basis, orthogonal transformation, the standard form of real symmetric matrices.
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