线性代数复习提纲（Review outline of linear algebra）.docVIP

线性代数复习提纲（Review outline of linear algebra） Review outline of linear algebra Part 1: basic requirements (calculation) The calculation of four order determinant; The calculation of the special determinant of order N (such as row, row, column, and equality); The operations of matrices (including addition, subtraction, multiplication, multiplication, transposition, inversion, etc.); Find the rank and inverse of the matrix (two methods); solve the matrix equation; A discussion on the solutions of linear equations with parameters; The solution of homogeneous and nonhomogeneous linear equations (including unique and infinite solutions); Discuss whether a vector can be expressed linearly with a vector group; Discuss or prove the relevance of vectors; Finding the maximal independent group of vectors, and expressing the redundant vectors linearly with maximal independent groups; The independent groups are orthogonal and modular; Seek eigenvalues and eigenvectors of a square; The diagonalization of matrices can be discussed if the matrix and diagonal matrices of similar transformations can be written; The diagonalization of symmetric matrices is made by orthogonal similarity transformation (orthogonal matrix); Write the matrix of the two type, and standardize the two order, and write the transformation matrix; Positive definite of two or symmetric matrices. The second part: basic knowledge Determinant 1. definition of determinant A notation consisting of n^2 elements AIJ is called a n order determinant. (1) it represents all possible algebraic sum of the product of n elements taken from different rows and columns; (2) the expansion of a total of n item, in which the symbol is half and right; Calculation of 2. determinant First order | alpha alpha |= determinant, two or three order determinant with diagonal rule; The calculation of order N (n=3) determinant: reduced order method Theorem: the value of the determinant of a n order is equal to the sum of the elements of any row (c